1. Background and introduction
Against the backdrop of sea level rise accompanying anthropogenic climate change, increasing attention has been drawn recently toward day-to-day sea level variability (Sheridan et al. 2019). While lunar and solar gravitational forcings are the biggest contributors to subdaily water level ranges for most locations, the nonastronomical portion of coastal water level variability is largely a function of the weather at various time scales (Anderson et al. 2019; Woodworth et al. 2019). When combined with astronomically forced high tides, this meteorological component to sea level has been shown in numerous prior studies to contribute to the non-storm-related, or sunny-day, “nuisance” floods that have plagued low-lying coastal towns, especially along the Atlantic coast of the United States (Sweet et al. 2014; Sheridan et al. 2017).
One of the more common atmospheric forcings is the inverse barometer (IB) effect (Piecuch and Ponte 2015; Pirhalla et al. 2022), whereby low atmospheric pressure leads to less force pressing downward on the ocean surface, thereby allowing the water level to rise, while high atmospheric pressure works oppositely. More important is the wind, relative to both onshore versus offshore flow direction (that would work similarly to that of a weak storm surge), and/or the longshore winds, either forcing sea surface water onshore (resulting in anomalously high water levels in areas of downwelling) or offshore (resulting in anomalously low water levels in areas of upwelling) along the coast via Ekman processes (Woodworth et al. 2019; Pirhalla et al. 2022). At longer time scales, seasonal variability can also play a role, via thermal expansion (Widlansky et al. 2020) and contraction of ocean water volume (Chen et al. 2000), subannual changes in large-scale ocean currents (e.g., the Gulf Stream; Ezer et al. 2013), and associated seasonal frequency or dearth of synoptic-scale systems that bring about the aforementioned IB effects, wind, and storm forcings. Even further out in time, interannual variability in nontidal water level anomalies has been linked to multiple phenomena, most prominently El Niño–Southern Oscillation (ENSO; e.g., Merrifield et al. 2012; Hamlington et al. 2015; Long et al. 2020).
While ample research has explored these varied relationships, accurate predictions of nontidal residual sea levels beyond the known skillful forecast limit of contemporary numerical weather models have remained elusive, despite their potential usefulness (Long et al. 2021; Jacox et al. 2020). Consequently, considerable efforts have been made recently toward improving the skill of subseasonal to seasonal (S2S) and longer forecasts (see, e.g., CPO 2017) and have led to the establishment of a joint NOAA–NASA effort toward this goal (NASA 2022). Stemming from these efforts, the increasingly predictable (but still imperfect) nature of ENSO (e.g., Widlansky et al. 2017), and the temporal inertia such atmospheric–oceanic modes of variability can sustain, has been particularly promising in terms of improving predictive skill of anomalous water levels (AWLs) at S2S lead times (Long et al. 2021; Shin and Newman 2021).
Situated within these ongoing projects, the current research has three primary aims. First, this study builds upon the daily scale research on the relationship between synoptic circulation patterns (CPs) and sea level variability that our group has explored in the past (Pirhalla et al. 2022; Sheridan et al. 2019, 2017), by expanding these methods to investigate whether similar relationships exist using monthly scale data. As a proof of concept, we examine two separate locations: San Diego, California (Pacific coast), and Charleston, South Carolina (Atlantic coast), both in the United States. Second, this research will examine the predictability of the predefined monthly scale synoptic circulation patterns and whether forecasting these categorical patterns is more skillful than 1) numerical forecast model output of the continuous field itself, 2) forecasts based on simple climatology, and 3) simple-persistence and damped-persistence forecasts (where persistence is multiplied by the autocorrelation at each lag). Finally, this research will investigate the relative utility of categorical patterns versus these other forecast types via an application of two pattern-based forecasting methods to predict anomalous sea levels over S2S lead times (defined herein as 1–9 months).
2. Data and methodology
a. Water level data and treatment
Monthly mean water level data were acquired from the Permanent Service for Mean Sea Level web page (https://www.psmsl.org/data/obtaining/) for two tide gauge locations in the United States for 1950–2019: San Diego, California (station 0158 at 32.713°, −117.173°), and Charleston, South Carolina (station 0234 at 32.782°, −79.925°). To eliminate seasonal variability, the average monthly sea level value for each of the 12 calendar months was calculated and then subtracted from each of the n = 840 months in the dataset. These monthly anomalies were then linearly detrended over the same time period, resulting in the AWLs used for the basis of this research.
b. Climate data and treatment
Spatial climate data were obtained from two sources. For developing the classification and training the artificial neural network (ANN) models below, monthly mean sea level pressure (SLP) and 10-m u and υ wind components were downloaded from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis for 1950–2019. For prediction, forecast data were obtained from the NOAA Climate Forecast System (CFS) model, version 1 (from 1982 to March 2011) and version 2 (from April 2011 to 2019). Archived monthly scale operational analyses (for lagged inputs) and 9-month operational forecasts were obtained from CFS for the same climate variables mentioned above. For both ERA5 and CFS data, the globe-wide and full-resolution data were first interpolated to an equidistant 10 242-point global-scale grid (to prevent oversampling at higher latitudes) and then geographically divided into subsets for ±15° latitude and ±15° longitude around each tidal gauge station in each direction. These 30° × 30° spatial domains were determined to best capture synoptic-scale variability around the tide gauge, without being so large as to incorporate atmospheric processes into the classification that might be unconnected to coastal sea levels, and to align well with prior research using synoptic patterns to examine sea level variability (e.g., Sheridan et al. 2019; Pirhalla et al. 2022).
Herein, following much of the same methodology described in Sheridan et al. (2019), who used daily scale atmospheric data for three different domains, circulation patterns were developed using monthly scale climate data for two domains. Prior to classification, the monthly mean (e.g., the mean of n = 70 Januaries from 1950 to 2019) was subtracted from the raw data. These monthly anomalies were then detrended and standardized for each grid point. This process was repeated separately for each of the grid points in each of the three datasets (SLP, u wind, and υ wind) for the two domains and for both the ERA5 and CFS datasets. Then, the separate u and υ wind datasets were concatenated into a single “wind” dataset prior to classification (herein referred to as 10mWIND).
Monthly teleconnection and oscillation data (Table 1) were also obtained from various sources, including the NOAA Physical Sciences Laboratory (PSL 2022), NOAA Climate Prediction Center (CPC 2022), and World Meteorological Society Climate Data Explorer (WMO 2022). These data were used to help explain sources of predictability.
Eta correlations between CPs and WPs and selected teleconnective oscillations. Bold and italicized values indicate statistical significance (p < 0.05). Datasets can be found at PSL (2022), CPC (2022), and WMO (2022). Note the abbreviations for the sources: BL87 is Barnston and Livezey (1987); RJ87 is Ropelewski and Jones (1987); E99 is Enfield et al. (1999); E01 is Enfield et al. (2001); B01 is Baldwin et al. (2001); WE01 is Wang and Enfield (2001); CPC23 is CPC (2023); and M02 is Mantua and Hare (2002).
c. Circulation pattern classification
The two z-scored datasets (SLP and 10mWIND) were each separately subjected to a common two-step procedure in synoptic climatology for pattern classification (Yarnal 1993; Lee and Sheridan 2015), whereby an s-mode principal component analysis (PCA) of the dataset is undertaken to reduce data dimensionality and collinearity of the spatial data, and principal component (PC) scores with eigenvalues greater than 1.0 were retained. These retained PCs were then used as inputs into a self-organizing map (SOM) clustering algorithm, which outputs a categorical value indicating the atmospheric (SLP or 10mWIND) pattern for each month in the time series. SOMs have become a common clustering technique in applied synoptic climate research over the last two decades and were chosen primarily due to their use in our research team’s prior investigations on daily scale sea level variability (e.g., Sheridan et al. 2019), but also due to the way SOMs can aid in visualizing the continuum of atmospheric patterns across two-dimensional space (Sheridan and Lee 2011). In addition to the single “winning” category, a distance matrix is output, whereby, for each row (month), the Euclidean distance between the retained PCs (representing the observed SLP/10mWIND field) and the centroid of each cluster is calculated, with the “winning” category being the cluster with the shortest distance. One of the consequential decisions when using SOMs is choosing the ideal “size” of the SOM, that is, how many nodes the SOM should have on each axis (e.g., a 5 × 6 SOM has five rows of nodes on one axis and six columns of nodes on the other and, thus, 30 total nodes/clusters/patterns). Multiple permutations of varying-sized SOMs were trialed for each domain and meteorological variable to see which size of SOM best partitioned water level data across the spectrum of patterns. The η correlations (described below) and standard deviations were used as metrics for these clustering validations. The resulting SOMs for SLP CPs and 10mWIND patterns (WPs) are displayed in Figs. 1–4.
SOM for Charleston anomalous SLP CPs. Units are in anomalous millibars (1 mb = 1 hPa).
Citation: Artificial Intelligence for the Earth Systems 2, 3; 10.1175/AIES-D-22-0057.1
As in Fig. 1, but for WPs. Anomalous vectors calculated separately for u and υ components (shown by arrows); the unsigned strength of the anomaly (colors) is the square root of the sum of the squared anomalous components.
Citation: Artificial Intelligence for the Earth Systems 2, 3; 10.1175/AIES-D-22-0057.1
As in Fig. 1, but for San Diego CPs.
Citation: Artificial Intelligence for the Earth Systems 2, 3; 10.1175/AIES-D-22-0057.1
As in Fig. 2, but for San Diego WPs.
Citation: Artificial Intelligence for the Earth Systems 2, 3; 10.1175/AIES-D-22-0057.1
d. Modeling weather–AWL relationships: NARX
The modeling process is outlined in Fig. 5. Potential predictor variables for modeling the weather–sea level relationships included the dummy/binary circulation pattern categories for each of the CPs and WPs, along with the retained PCs used for each SOM (all based upon ERA5 climate data). These potential predictor climate variables were subjected to an input variable selection (IVS) procedure that utilized principal component analysis and Spearman correlations to limit predictor variables in the model to only the resulting PC scores that had statistically significant (p < 0.01) Spearman correlations. Those variables making the cut were then used as the final predictor variables in the subsequent modeling.
Flowchart outlining the ordered steps for NARX modeling of anomalous water level data for each location.
Citation: Artificial Intelligence for the Earth Systems 2, 3; 10.1175/AIES-D-22-0057.1
Modeling of the relationship between climate and AWLs was done using nonlinear autoregressive exogenous input (NARX) models. For brevity, we refer readers to Sheridan et al. (2019), and references therein, for more detailed information on NARX models in the context of sea level modeling. Briefly, NARX models are ANN time series models that use past values of the predictand variable (the anomalous water levels), along with present and past values of the predictors (the significant PCs of the weather-based variables from the IVS process described in the paragraph above), in order to learn (and predict) the next value of the predictand.
Multiple NARX model architectures were trialed with varying amounts of lags and neurons. Further, since NARX models are randomly initialized, a set of 20 ensemble members for each location were trained, and the ensemble median value was calculated as the final output. Training of each member model was completed on the first 60% of the data; the next 20% of the data were held out for internal validation, and the last 20% of the data were held out for “external testing.” Training proceeded using Levenberg–Marquardt (Hagan and Menhaj 1994) optimization and internal validation (also known as early stopping). Internal validation is an overfitting prevention technique, whereby, at each training update, the resulting trained model is run on a separate “internal validation” time block of the data to determine whether the model improves [lower root-mean-square error (RMSE)] for that block; if it fails to improve six consecutive times, then the model trained six update steps ago is considered optimal, as it is generalizable across at least one other portion of the data (i.e., a portion of the data that was not used for training). The mean bias (calculated on the training portion of the dataset) at each lead time was then subtracted from the resulting AWL output from the model. The bias-corrected output of the final 20% of the dataset (i.e., that portion held out for external testing) is used to determine what the best NARX model architecture is for each location (lowest RMSEs); ultimately, NARX models with nine predictand lags and four neurons were used for San Diego, and models with nine predictand lags and seven neurons were used for Charleston.
Once SOMs are created with ERA5 data and the NARX models are fully trained using ERA5-based climate input (i.e., the PCs, CPs, and WPs), the entire process is then repeated using the CFS data. First, raw CFS forecast data interpolated to the same 10 242 global locations are divided into subsets to the same 30° latitude–longitude domains, detrended, deseasonalized, and standardized (using the saved monthly means and standard deviations from ERA5). These standardized anomalies are then multiplied by the saved loadings/coefficients from the PCA described in section 2c, transforming them into “virtual PCs.” These PCs were then run through the saved SOM models to compute CP and WP forecasts from the CFS data (note that these forecasted CPs and WPs are used for the results in section 3b). These forecasted patterns and PCs from CFS are then used as inputs into the pretrained (on ERA5 data) IVS process and NARX models, outputting a forecasted water level. Finally, this output value is bias corrected using the mean bias calculated from the training portion of the data (see paragraph above), yielding the final forecasted AWLs. The NARX model performance statistics reported in section 3c below are based upon these forecasted AWLs from 2012 through 2019 (roughly the last 20% of the AWL dataset) in order to align with the independent “external testing” time block of the dataset that was set aside when the model was trained.
e. Alternative weather–AWL forecast; PLANN
Numerical forecast models like CFS have known limitations at S2S lead times (Fan et al. 2021). Considering the results that will be discussed in section 3a below showing that WPs and CPs have strong and significant relationships with sea level anomalies, along with those in section 3b showing the dropoff in CFS skill at predicting WPs and CPs at longer lead times, we hypothesize that the NARX model performance may be hindered by the use of CFS forecast model output to derive patterns (that are then utilized further downstream to predict AWLs). To explore this theory, we examine an alternative forecasting method that bypasses the numerical forecast model (CFS) data altogether. Instead of using CFS-based forecast data to predict future WPs and CPs and then running them through a NARX model, for this alternative method, we simply train ANNs to learn 1–9-month lagged relationships between the AWL data and observed (ERA5) SOM patterns from the month prior. We refer to this forecasting method as a pattern-based lagged ANN (PLANN) forecast.
Similar to the NARX models, to prevent overfitting, these PLANN models are trained on only the first 60% of the data, with the last 40% of the data held out for internal validation (20%) and external testing (20%), respectively. We train separate cascade-forward ANN models for each lead time and location. Input predictor variables are the distance matrices (described in section 2c) of the SOM CPs and WPs from the month prior to initialization and the observed AWL of the prior month. So, for example, if it is 1 July, and we are initializing forecasts for the next 9 months, then the inputs for all nine models would be June’s observed SOM distances and June’s observed AWL. We trialed 500 models with between one and five neurons (100 with each) and chose the PLANN model with the lowest RMSE for each location and lead time.
f. Statistical analyses
Univariate analyses of the historical relationship between AWLs and the two sets of atmospheric patterns were undertaken using three metrics. Categorical η correlations were used to quantify the relationship between AWL variability and SOM classification as a whole. Based upon traditional ANOVA tables, the η correlation is simply the (positive) square root of the between-type sum of squares over the total sum of squares (see Smith et al. 2020). The η values range from η = 0 to η = 1 and can be interpreted similarly to an absolute value Pearson correlation, with higher values (closer to η = 1) indicating that the set of atmospheric patterns have an increasingly large effect size on AWLs (i.e., that the SOM patterns are important predictors of AWL fluctuations). Statistical significance (η ≠ 0) is determined using the F statistic from ANOVA as well.
Then, to assess AWL–weather relationships on a pattern-by-pattern level, two other metrics were examined: 1) mean AWL by pattern (and 95% confidence intervals of the mean) and 2) relative risk (RR) of a high-water event (HWE). To get an adequate sample size of events, we defined an HWE as a month with an AWL at the 90th percentile or higher of all AWLs in the tide-gauge dataset (which is +64 mm for San Diego and +90 mm for Charleston), resulting in 46 and 47 HWEs for each location, respectively. As described in Pirhalla et al. (2022), the concept of RR has its origins in public health literature and stems from a standard 2 × 2 contingency table. The relative risk (also known as the risk ratio) is the probability of an HWE occurring when a particular pattern does occur divided by the probability of an HWE occurring when that pattern does not occur. RRs are interpreted as the x-fold increase/decrease in the likelihood of the HWE happening, given the occurrence of a particular pattern, and are statistically significant when the 95% confidence interval of the RR does not span 1.0. Finally, the forecast skills of all methods are quantified using two metrics: Spearman correlation (ρ) and median absolute error (MdAE) of the AWL.
3. Results and discussion
a. Historical (ERA5) atmospheric pattern and AWL relationships
The resulting CPs and WPs developed for each region are shown in Figs. 1–4. The two-dimensional structure of the SOM helps display the general breadth of patterns across the domain and the main modes of variability. For example, with the Charleston SLP SOM (Fig. 1), the SLP anomalies generally decrease as one moves from left to right across the SOM, and the major centers of anomalous pressure generally are more westward as one moves from top to bottom across the SOM. As such, CP-1 is quite similar to CP-2 (both could be broadly defined as Gulf highs) but quite different from CP-30 (a broad northeastern low) along one diagonal axis, in the same way CP-25 (broad northeastern high) and CP-6 (northern plains low) are dissimilar along the opposite diagonal. Monthly scale circulation pattern occurrences are significantly related to various low-frequency modes of variability (or teleconnective oscillations; Table 1). Along the West Coast, the strongest of these modes are the SOI and PDO in forcing anomalous SLP patterns, along with the influence of the Pacific–North American (PNA) pattern and the east Pacific–North Pacific (EPNP) pattern in forcing WPs. While all of the aforementioned modes also influence atmospheric patterns on the Atlantic seaboard, they generally play a smaller role than the NAO and the Arctic Oscillation (AO), while the tropical North Atlantic (TNA) index also figures significantly.
The benefits of an SOM-based visualization of atmospheric circulation are apparent when examining the AWL response associated with each pattern and “mapped” similarly across SOM space (Fig. 6). As noted in prior research (Sheridan et al. 2019, 2017; Pirhalla et al. 2022), the meteorological forcing of shorter-term sea level variability is often threefold: 1) the IB effect, 2) direct onshore versus offshore winds, and 3) longshore winds (relative to being parallel to the shoreline). Accordingly, for the Charleston SLP SOM, the CPs with low pressure in the area of the tide gauge (in the upper-right portion of the SOM) are often associated with higher AWLs (up to +87 mm; p < 0.05) and a significantly increased risk of HWEs (up to RR = 5.3; p < 0.05). Conversely, high pressure CPs, especially those centered south and/or east of the gauge (e.g., on the bottom row of the SOM and left side of the SOM), are associated with below-normal AWLs and nearly no risk of HWEs. Associations between WPs and AWLs are a bit more complex. Two different situations lead to increased risk of high water level anomalies, either anomalously stronger onshore winds from the southeast, such as in WP-31 and WP-32, or a more northeasterly component to the winds than normal (often due to a passing cyclone), such as in the entire lower-right corner of Fig. 2. This NE flow direction likely induces high AWLs via onshore sea surface currents and downwelling caused by Ekman transport.
(left) Mean AWLs (mm) by SOM pattern and (right) RR of an HWE by SOM pattern. Bold, italicized, and underlined values are statistically significant (p < 0.05). Darker shades of blue (orange) indicate increasingly large (small) values.
Citation: Artificial Intelligence for the Earth Systems 2, 3; 10.1175/AIES-D-22-0057.1
For San Diego, quite similar relationships are noticed, though the water levels appear to be more influenced by SLP than by wind stress (Table 2). The left-hand side of the SLP SOM (Fig. 3) hosts nearly all offshore low pressure CPs and, thus, all of the patterns with significantly increased risk of HWEs, exemplified by CP-1, which features a strong low likely centered over the Gulf of Alaska that is associated with nearly an eightfold increase in the likelihood of an HWE and a +79 mm (p < 0.05) AWL on average. With WPs, the right side of the SOM (Fig. 4) exhibits more southerly and southeasterly components to the winds of various magnitudes, situations that would catalyze onshore flow from both wind stress and Ekman transport, which both translate into above-average AWLs. Such atmospheric setups may also accompany atmospheric rivers, which have been shown to contribute to West Coast flooding events as well (Piecuch et al. 2022). On the other hand, the left side of the wind SOM has mostly anomalously anticyclonic wind and/or a northerly/northeasterly component to flow than normal, leading to below-normal sea levels, with virtually no risk of HWEs. The lone exception is WP-12, which boasts a 5.3 times increased risk of an HWE. While not obvious, this anomaly for WP-12 is perhaps due to a fairly nebulous cyclonic circulation that appears centered over the Southern California coast and ushers in due-westerly winds to San Diego. Unlike along the Atlantic coast, along the West Coast, it is more likely that all three of the common meteorological forcing agents for high water [i.e. below-normal barometric pressure, stronger onshore wind components, and Ekman-inducing (in this case, southerly/southeasterly) wind components] are occurring in unison (e.g., as a cyclone moves through the U.S. Pacific Northwest), or at least within a few days of each other, keeping water levels high for a longer period of time and increasing the chances of an HWE month. Indeed, both the low pressure patterns and cyclonic wind patterns leading to anomalously high AWLs are much more persistent on the West Coast than the same patterns are along the East Coast (see the online supplemental material).
Categorical correlations (η) between anomalous sea levels at Charleston and San Diego and either SLP SOM (CPs) or wind SOM (WPs). All correlations are statistically significant (p < 0.001).
b. Atmospheric forecasting of CPs and WPs
The predictive skill of predefined monthly scale atmospheric patterns varies by location, lead time, and variable. In terms of error (MdAE), predicting categorical circulation patterns shows unanimous improvement over the CFS model forecast of the seasonally relative detrended anomaly (referred to as the CFS-DA forecast herein; Fig. 7). This improvement is most noticeable for WPs, for which the forecasting of patterns yields smaller errors (for both u and υ winds) at all 9 months of lead time than the output of CFS-DA fields at any month of lead time for both locations. Pattern forecasts are more skillful than simple-persistence forecasts of u and υ winds at all lead times in both locations, though they are less skillful than any type of persistence forecast for SLP in both locations at nearly every lead time. Note that due to low monthly scale autocorrelation, damped-persistence CP and WP forecast skill is nearly identical to that of climatology. And while the pattern forecasts largely outperform CFS-DA forecasts and simple persistence, all three forecasting methods struggle compared to a simple climatology forecast (and therefore, damped persistence). This said, pattern forecasts show some potential for the nearer-term (0 month) forecast lead times, exhibiting smaller errors than the climatology forecast for certain geographic areas (Table 3). Of the six domain–variable combinations, relative to climatology, the pattern forecasts are best for winds in the Charleston domain, especially zonal winds over the northeastern Gulf of Mexico and meridional winds over the Sargasso Sea (supplemental material). These areas of superiority of pattern forecasts over climatology are generally areas with ample variability in the first place (relative to other parts of the domain), which naturally are going to return larger error values when using a climatology forecast.
MdAEs for (left) San Diego and (right) Charleston for (top) SLP, (middle) u wind, and (bottom) υ wind for various forecasting methods at 0–9 months lead time: pattern forecast (blue line), CFS-DA output (orange), climatology forecast (Climo; gray), simple-persistence forecast (SimpPersist; yellow), and damped-persistence forecast (DampPersist; black dashed).
Citation: Artificial Intelligence for the Earth Systems 2, 3; 10.1175/AIES-D-22-0057.1
Percentage of locations within each domain where the median absolute error for the pattern forecast is better than that of the climatology forecast. Numbers 0–9 refer to lead months.
Anomaly correlation performance is a bit more nuanced than MdAEs. The CFS-DA correlation is better than that of pattern forecasts for most locations. Relative to CFS-DA performance, however, the pattern forecast correlations come closer to parity at longer lead times and even start to show better skill in certain locations, especially for meridional winds (supplemental material). Despite being an improvement over the CFS-DA forecasts for these locations, the magnitude of these correlations at these longer lead times is still fairly low (i.e., ρ ∼ 0.05–0.15), implying limited real-world utility. At shorter lead times, the SLP pattern forecasts over the open Atlantic (in the Charleston domain) and the open Pacific (in the San Diego domain) do show improvements over CFS-DA.
Taken together, the results above indicate that for monthly scale to seasonal-scale forecasting of SLP and 10-m winds in these two regions, a simple climatology forecast is more skillful than other methods examined, including the output of the CFS model, at least for the domain-wide averages. It has been well documented that the skillful prediction limits of today’s numerical atmospheric models are often somewhere between 3 and 6 weeks (Albers and Newman 2019), and therefore, the low skill of the monthly and longer-scale forecasts evaluated herein are not surprising. For example, in evaluating two large-scale atmospheric variables (200- and 500-hPa heights), Weber and Mass (2017) found that forecast skill fell below that of climatology at lead times longer than 2 weeks. Despite this, pattern-based forecasts were nearly always more skillful than CFS-DA output and simple persistence and could even improve upon climatology at some locations and lead times, especially for 10-m winds. Future research that integrates categorical pattern-based forecasts into other domains and atmospheric variables, especially at submonthly lead times, may be worth exploring.
c. Sea level forecasts
Tables 4 and 5 display the error performance statistics (MdAE and ρ) of the various types of AWL forecasts. As to be expected, NARX models for both locations show higher skill at the shortest lead times (lead 0 and lead 1). For all lead times, and for both performance metrics, the NARX models are substantially better in San Diego than in Charleston, exhibiting ρ > 0.5 for both lead 0 and lead 1 month in San Diego. The NARX model forecasts are generally more skillful than a simple climatological mean AWL forecast when it comes to MdAE. However, the NARX models are poorer than a damped-persistence forecast for most lead times and locations when it comes to MdAEs, but they do show some relative improvement (over other forecast methods) when it comes to correlations at longer lead times in Charleston.
MdAEs (mm) of multiple types of sea level anomaly forecasts by lead time (months, along horizontal axis) for San Diego and Charleston for the testing portion of the study period. AWL-climo is the simple climatology–forecasted AWL; damped persistence is the damped-persistence forecast of “current” AWL out 1–9 months; full NARX (w/CFS) is the NARX-based forecast using CFS forecast data to compute SOMs; and PLANN is the pattern-based lagged ANN forecast. Bold and italicized values indicate the best model at each lead time. Cells marked with “x” at lead 0 are not considered valid forecasts because of the way the forecast is constructed.
As in Table 4, but for Spearman’s rho (ρ) correlations of multiple types of AWLs. Note that there is no correlation for a climatology anomaly forecast.
In an effort to determine if the results of the NARX models with CFS-derived patterns described above could be further improved at longer lead times (i.e., when CFS model output is known to be less skillful), the PLANN forecasting method was also examined (described in section 2e above). Results show that the PLANN forecasts show improved skill over climatology at many of the lead times and also are often better than the NARX models for both MdAE and correlation. In San Diego, the PLANN forecast is better than climatology (by ∼7 mm on average) and damped persistence (by ∼1.2 mm on average) at nearly every lead time. In Charleston, the damped-persistence forecast is the most skillful in terms of both MdAE and correlation at 1 and 5 months of lead time, but it yields to one of the other forecasts at other lead times. However, even in Charleston, the PLANN forecast outperforms damped persistence when averaged across all lead times (by 1.4 mm) for MdAE. In all, the pattern-based forecasts (either NARX or PLANN) are best for seven of the nine valid lead times in San Diego and five of the nine lead times in Charleston for MdAE.
Since CPs and WPs are significantly related to some teleconnective oscillation indices, the forecast skill of the NARX models likely stems partly from the skill in forecasting key teleconnections in dynamical models such as CFS, especially ENSO (Kirtman and Min 2009; Barnston et al. 2019), considering its outsized role in modulating sea levels (Holbrook et al. 2020). This said, as shown by the correlations in Table 1, the CPs and WPs are far from being “fully explained” by these modes of variability. Moreover, since the PLANN forecasts are independent of CFS and yet more skillful than NARX, albeit only slightly, this suggests that there is at least some predictable nonteleconnection component captured within the synoptic-scale patterns that stands to aid longer-term forecasting of sea levels.
The skill of pattern-based methods (NARX and PLANN) at forecasting sea level anomalies is an encouraging step toward improving S2S forecasts of water levels. These results also underscore our impetus behind exploring this line of environmental prediction (i.e., predictions based upon categorical patterns). We hypothesize that forecasting using patterns is inherently an ensemble forecast; that is, we are predicting within a category (a wind pattern or a pressure/circulation pattern) that encompasses a range of different possibilities for the atmosphere, much as an ensemble approach would. Moreover, this category itself (along with its inherent range/variability) carries forward meaningful statistical relationships with regard to water levels (as shown in Fig. 6) into the predictive ANN model. In other words, we do not need to have an atmospheric forecast be exactly right to get more skillful predictions of water levels; we really only need to know generally what range of possibilities the prediction falls within [represented here by a categorical variable (the pattern)] to give a skillful forecast of anomalous water levels.
4. Summary and conclusions
This research examined the relationship between monthly scale sea level variability and atmospheric circulation patterns for two different locations in the United States: San Diego, California, and Charleston, South Carolina. Building upon prior research showing that SLP and near-surface wind patterns can modulate the nonastronomical component of daily sea level variability (Pirhalla et al. 2022; Sheridan et al. 2019, 2017), we find herein that similar meteorological forcing happens with monthly scale variability as well. Generally, months with anomalously low atmospheric pressure patterns are associated with an increased risk of high-water events, and vice versa. For winds, monthly averaged patterns exhibiting either stronger onshore wind direction or alongshore wind components in the direction that induces Ekman downwelling (i.e., south-to-north winds along the Pacific coast and north-to-south winds along the Atlantic coast) are significantly related to higher water levels.
These historical relationships were used as a foundation upon which to train an ensemble of NARX models to examine the predictability of anomalous monthly water levels at lead times up to 9 months into the future. While these models showed improvement over simple climatology forecasts, they were largely inferior to a damped-persistence forecast. As expected, the NARX model skill generally deteriorated at longer lead times, coming closer to parity with climatology and damped persistence.
However, to overcome the potential limitations of forecast model output at longer lead times, we explored a second method of pattern-based and ANN-based forecasts of water levels. This simpler method used lagged relationships between prior observed atmospheric patterns and water levels in order to bypass CFS forecast output altogether. On average, these pattern-based lagged artificial neural network (PLANN) models were more skillful than the other forecast types, including damped persistence, in both locations, but especially in San Diego. These results support the notion that sea level forecasts at S2S lead times can be improved through the combined use of categorical atmospheric patterns and ANN modeling.
Since contemporary numerical forecast models are known to have limitations at longer lead times, a secondary aim of this research was to investigate how this limitation manifests when forecasting a predefined categorical pattern, as opposed to the postprocessed output of that forecast model itself. Our results indicate that forecasting categorical patterns leads to substantially less absolute error than forecasting the seasonally relative detrended anomaly field itself (at least for CFS), for both SLP and 10-m winds. Compared to a simple-persistence forecast, the pattern forecasts are better for 10-m winds at all lead times but slightly worse for SLP, especially in San Diego. This said, for monthly and longer lead times, a simple climatology forecast or a damped-persistence forecast is superior to other forecast types (simple-persistence, numerical model output, or pattern forecasts), though there are some portions of the two domains where pattern forecasts are more skillful even than climatology. Considering that the pattern forecasts are best (relative to climatology) in the nearer term, and in areas with a higher amount of atmospheric variability, examining the skill of pattern-based forecasts for shorter-term (submonthly; 0–4 weeks) lead times and/or in higher-latitude regions (with more inherent atmospheric variability) may prove worthwhile for improving forecast skill at the leading limit of current numerical model capabilities. Alternatively, combining methods, using damped persistence as the baseline forecast and then adding a PLANN-based model to “nudge” that baseline forecast, could yield more skillful predictions.
Ultimately, this line of research may aid in the real-time prediction of high-tide flooding events that result in critical infrastructure damage, habitat and shoreline alteration and losses, and a host of other impacts along U.S. coastlines (Sweet et al. 2021). Many operational high-tide flooding S2S prediction efforts rely solely on climatology and trend projection. The skill demonstrated by the PLANN forecasts in particular suggests that incorporating this or similar methods can improve upon existing climatological approaches for lead times of up to 9 months and thus may lead to the development and transfer of new forecast tools to support NOAA mission–oriented products and services and for coastal-climate resilience purposes (e.g., Dusek et al. 2022). Indeed, such categorical perspectives on forecasting, that is, using weather patterns, have already gained traction in various applications in the United Kingdom (Neal et al. 2018; Richardson et al. 2019) and India (Neal et al. 2022), among other locations. In addition to exploring NARX and PLANN forecasts at shorter lead times and different locations, the inclusion of different atmospheric variables (other than SLP and 10-m winds used exclusively herein) may prove useful in future research. For example, our methods did not directly incorporate low-frequency oscillation/teleconnection indices into modeling. Though the SOM pattern frequencies are significantly related to them (e.g., see Table 1), future research may benefit from the direct inclusion of these indices in PLANN-like water level forecasts. In addition, the application of machine learning and ANNs in environmental sciences is still in its relative infancy, and different ANN modeling methods (e.g., long short-term memory ANNs or gated recurrent unit ANNs, among others) should also be explored. Future research should also examine if a “pattern-based perspective” on climate-related environmental forecasting may be useful in other applications.
Acknowledgments.
The authors thank the editor and the anonymous reviewers for providing constructive feedback, comments, and suggestions, leading to a better paper. Funding for this research has been provided by the CPO of NOAA, Federal Award NA17OAR4310113. The authors declare no conflicts of interest.
Data availability statement.
All data for this research have been made publicly available at the Mendeley Data Repository, accessible at https://doi.org/10.17632/4c4dshr2mb.1 (Lee et al. 2022). Data can also be retrieved from the author upon request.
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