On the potential use of weather types to describe the interannual variability of annual maximum discharge across the conterminous United States

Weather types or weather regimes represent the dominant modes of large‐scale atmospheric circulation patterns and have been used to understand and explain the physical mechanisms of different weather events. While there have been many studies that analyse the changes in extreme climate events through the lenses of weather typing, there is a lack of studies that attribute changes in flood extremes to changes in weather regimes. Here we examine the potential applicability of weather types as predictors of flood extremes. For 4535 streamgages across the conterminous United States, we employ a statistical attribution approach to model the seasonal and annual maximum discharge, utilizing five weather types with distinct synoptic features. Although there are regional patterns in the relationship between weather types and the major climate drivers of flooding, our results show that the frequency of weather types does not provide enough information to model the interannual variability in the magnitude of flood peaks across the conterminous United States.


| INTRODUCTION
Weather types (WTs; or weather regimes) provide a classification of large-scale atmospheric circulation patterns defined by a single or multiple hydro-dynamic variables such as geopotential height, sea level pressure or wind field.Since the WTs represent the dominant modes of atmospheric flow, they enable the understanding of the physical mechanisms of weather features (e.g., air pressure, temperature, precipitation and wind) at a synoptic scale (e.g., Coleman & Rogers, 2007).This weather-typing approach has also been utilized to understand and account for various weather-related hazards such as wildfire (e.g., Labosier et al., 2015), air pollution (e.g., Hebbern & Cakmak, 2015;Tso et al., 2022), heat-related mortality (e.g., Fonseca-Rodriguez et al., 2019;Huang et al., 2020) and wind resource (e.g., Millstein et al., 2019;Yang et al., 2022).
The identification of WTs varies in space and time (e.g., seasons and extreme events) based on the specific focus of a given study.In the United States, there have been many studies to characterize daily WTs and analyse them in terms of temperature and precipitation patterns (e.g., Agel et al., 2018;Barlow et al., 2019;Casola & Wallace, 2007;Coe et al., 2021;DeLaFrance & McAfee, 2019;Grotjahn et al., 2016;Loikith et al., 2017;Roller et al., 2016;Vigaud et al., 2018;Zhang et al., 2022;Zhang & Villarini, 2019).For instance, Coe et al. (2021) and Roller et al. (2016) identified distinct WTs for temperature/precipitation during fall and winter seasons, respectively, in the U.S. Northeast.Agel et al. (2018) also analysed WTs in the same region but focused on extreme precipitation days.Loikith et al. (2017) characterized the winter and summer synoptic-scale patterns over the northwestern United States to physically interpret extremes in local temperature and precipitation.Zhang and Villarini (2019) identified five WTs for the spatial domain covering the conterminous United States (CONUS) and examined the effect of the WTs on precipitation across the U.S. Midwest.
Based on this brief review, WTs can provide useful information to understand the synoptic drivers of climate variables like precipitation and temperature.Given that these two variables are the fundamental drivers of flooding through their connection to various contributing factors such as antecedent wetness (Kim et al., 2019;Wasko & Sharma, 2017), snowmelt (Li et al., 2019;McCabe & Clark, 2005) and evapotranspiration (Rossi et al., 2016) as well as surface runoff, one research question that has received limited attention in the literature is the suitability of WTs in describing the changes in flooding by modulating precipitation and temperature (e.g., Armon et al., 2018;Camus et al., 2022;Gilabert & Llasat, 2018;Knighton et al., 2019).In the United States, Knighton et al. (2019) identified teleconnections between synoptic-scale climate variables and precipitation and discharge extreme events over the eastern United States, suggesting that geopotential height and integrated vapour transport are key variables for regional patterns of extremes.Camus et al. (2022) characterized 49 daily WTs in the eastern United States and identified a few dominant patterns associated with coastal compound flood events that occurred along the coast lines in the Gulf of Mexico and the U.S. East Coast.
Since the large-scale atmospheric circulation patterns can drive processes promoting the occurrence of weather extremes, the frequency of WTs is an important factor for the predictions of extreme events.Although there have been various studies about the trends in the frequency of WTs to identify the temporal changes in extreme weather events (e.g., Agel et al., 2021;Francis et al., 2018;Lee & Sheridan, 2018;Prein & Mearns, 2021;Zamir et al., 2018;Zhang et al., 2022;Zhang & Villarini, 2019), there is a lack of studies that attribute changes in flood extremes to the frequency of WTs: this study aims to examine whether WT frequencies can be used as predictors to capture the year-to-year changes in annual maximum discharge.For this purpose, we used the statistical framework developed by Kim and Villarini (2023), which allows the modelling of seasonal and annual maximum daily discharge in terms of its predictors (i.e., WTs).We then evaluated the performance of these models in describing the interannual variability of extreme discharge across CONUS.

| Datasets
Observed mean daily discharge series were obtained from 1949 to 2019 (the start year depends on data availability) for 4535 USGS streamgages across CONUS, where the observations are available for at least 30 years (i.e., we define 'a year' as one that has less than 10% of missing values) of the recent 40 years (i.e., 1980-2019).For modelling of the seasonal maximum discharge, we use a block maxima approach, in which we select the largest daily value for each season (i.e., block).In terms of predictors, we considered the five WTs defined by Zhang and Villarini (2019) and updated by Zhang et al. (2022) because they describe well different physical mechanisms responsible for precipitation and temperature patterns.These five WTs feature distinct large-scale meteorological patterns in the daily 500-hPa geopotential height anomaly and moisture transport from 1948 to 2019 over CONUS.We calculated the frequencies (i.e., the number of days) of WTs for each season and used them as predictors when modelling the seasonal maximum discharge.

| Identification of relationship between WT frequencies and climate drivers
Before developing statistical models for seasonal maximum discharge, we explored the relationship between the frequency of WTs and two major climate drivers of flooding (i.e., precipitation and temperature).
We obtained the season-averaged monthly total precipitation (mm) and monthly mean temperature ( C) from the Parameter-Elevation Regression on Independent Slopes Model (PRISM) dataset T A B L E 1 Summary of the relationship between the parameters of the full gamma or zero-adjusted gamma model (i.e., including all five WTs as predictors).

Distribution parameter
Formulation Probability at zero (ν) (where applicable) The μ and σ parameters are related to the concurrent and lag predictors by means of a logarithmic link function, while the ν parameter through a logit function for only the WTs in the concurrent season.(Daly et al., 2002;Daly et al., 2008).We then calculated the Spearman correlation coefficient between the seasonal frequency of WTs and the season-averaged precipitation and temperature for each grid cell.

| Statistical modelling
To develop nonstationary models of seasonal and annual maximum discharge, we followed the statistical attribution approach developed by Kim and Villarini (2023) utilizing the Generalized Additive Model in Location, Scale, and Shape (GAMLSS; Rigby & Stasinopoulos, 2005).
More specifically, we used the gamma distribution whose location (μ) and scale (σ) parameters are modelled using the frequency of WTs in the concurrent season (F.WT con ).To address the antecedent conditions that could lead to flooding (e.g., soil moisture, snowpack), we also included the frequency of WTs prior to the concurrent season (F. WT lag ).Because the gamma distribution is defined only for positive values, we modelled the μ and σ parameters of the gamma distribution using a logarithmic link function to ensure their positive values as below: F I G U R E 1 Correlation maps showing the relationship between observed precipitation and the frequency of weather types (on the rows) for each of the four seasons (on the columns).
When there are zero discharge values in the observations, we used the zero-adjusted gamma distribution, which has an additional parameter (ν) accounting for the probability of occurrence of zero-discharge values.The ν parameter was modelled using concurrent predictors and the logit link function as below: For each streamgage and each season, we fitted a full model that uses all five WTs (see Table 1) and its nested models depending on the linear combination of predictors, and selected the best one using Schwarz's Bayesian criterion (SBC; Schwarz, 1978).
F I G U R E 2 Correlation maps showing the relationship between observed temperature and the frequency of weather types (on the rows) for each of the four seasons (on the columns).
For each site, to combine four seasonal models and obtain the distribution of annual maximum daily discharge series, we conducted Monte Carlo simulations to mix the four selected seasonal models.
For each year, we first generated one value from each of the seasonal models, and then selected the largest one to be the annual maximum daily discharge.We repeated this 1000 times to get the mixture of the four seasonal distributions.We then performed these steps for each year in the record (see Kim and Villarini (2023) for details).
To assess the model performance in describing the interannual variability in extreme discharge series, we calculated the Spearman correlation coefficient between observations and the median of the modelled seasonal and simulated annual maxima.

| RESULTS AND DISCUSSION
We first identify the relationship between the WTs and two major climate drivers responsible for flooding.Figure 1 shows the correlation between the frequency of WTs and precipitation for each season.
Although the results show varying regional patterns depending on WTs and seasons, general regional patterns across all seasons for each WT can be explained by each of the synoptic features of WT.For (negative) geopotential height anomalies tend to have strong positive (negative) correlations between the WT frequency and temperature.
This result is consistent with Kożuchowski et al. (1992), who showed the strong correlations between seasonal temperature and 500-hPa geopotential height.
The abovementioned results indicate that there is a statistical relationship between WTs and precipitation and temperature, two drivers that were found to drive the interannual variability in seasonal and annual maximum discharge (Kim & Villarini, 2023).Is the information content in the WTs sufficient to make them useful as predictors to describe seasonal maximum discharge?Or, is this connection too tenuous, requiring the use of precipitation and temperature directly?correlation between the WT frequency and precipitation (Figure 1) to assess whether the selected covariates are reasonable to reflect the main climate driver.There are discrepancies in the regional patterns between what observed from the covariate selection (Figure 4) and relationships between WT frequency and precipitation (Figure 1).For instance, although WT1 generally shows a positive correlation with precipitation across the central and eastern United States (Figure 1), the WT1 is rarely selected in this region, regardless of the season (Figure 4).The WT3 and WT5 also show a discrepancy, with a strong positive correlation with precipitation in the U.S. West Coast particularly in the fall and winter seasons (Figure 1), but with a negative or zero coefficient for WT3 and WT5 at most of the streamgages in the area (Figure 4).In terms of lagged WTs (Figure 5), the spatial patterns are different from those of concurrent WTs, but it is still hard to explain the connection between flooding and its fundamental climate drivers.These discrepancies in spatial patterns indicate that the frequency of WTs is not enough to describe the interannual variability in flood extremes as a proxy of climate drivers.(middle and bottom panels), we do not observe any difference between these two groups, consistent with other studies (e.g., Ficklin et al., 2018;Kim & Villarini, 2023) that showed that the changes in annual maximum discharge are largely driven by changes in the climate system.

| SUMMARY AND CONCLUSIONS
In this study, we investigated the potential applicability of large-scale atmospheric circulation patterns towards the modelling of seasonal and annual maximum mean daily discharge.We considered five WTs with distinct large-scale meteorological patterns across CONUS and used their frequencies as predictors of seasonal and annual maximum discharge.The main conclusions of this study can be summarized as follows: • The correlation between the frequency of WTs and precipitation and temperature shows regional patterns, consistent with the physical characteristics of each WT.There is more regional structure in the correlation between WTs and temperature than precipitation.
• The seasonal models using the frequency of WTs as predictors show limited performance in capturing the interannual variability of seasonal maximum mean daily discharge, with 75% of all sites having a correlation coefficient of less than $0.4.This limited skill translated in limited performance in reproducing the annual maximum daily discharge, regardless of whether the basin was a reference site or not.
• The frequencies of concurrent and lagged WTs are inadequate to capture the magnitude of seasonal flood peaks as a proxy for climate drivers, with discrepancies in the spatial patterns between their covariate selections and relationships with fundamental physical drivers of flooding.
The WT accounts for the physical mechanisms of various weather phenomena at a synoptic scale so that its frequency can be a useful predictor of temporal changes in extreme weather events.In this study, however, we found that the WT frequencies have limitations when used to quantitatively describe the changes in the magnitude of flood extremes.One possible explanation is that the relationship between synoptic-scale WT and floods is too tenuous to capture the interannual variability in seasonal and annual maximum discharge, whose generating mechanisms are much more complex; as shown in Figures 1 and 2, WTs and precipitation/temperature are correlated, but not so strongly (especially for the case of precipitation, which is the major driver of flooding), leading to a reduction of information content as we go from WTs, to precipitation/temperature, to flooding.
Overall, our findings suggest that the frequency of WTs within our statistical attribution approach may not be suitable to describe the interannual variability in annual maximum discharge across CONUS, but that it could provide more of a high-level and qualitative information.
F I G U R E 6 Maps and boxplots showing the value of the Spearman correlation coefficient between observations and the median of the simulated distribution of the annual maxima for all (top panel), reference (middle panel) and non-reference (bottom panel) sites according to their classification in the GAGES-II dataset.In the boxplots, the limits of the box represent the 25th and 75th percentiles, while the line inside of it the median; the limits of the whiskers span the 5th and 95th percentiles.
instance, WT1 features a high-pressure over the North Pacific near the northwestern United States and strong moisture flux transport from the Gulf of Mexico to the northeastern United States(Zhang & Villarini, 2019), resulting in heavy precipitation across the central and eastern United States.Overall, negative correlations between the frequency of WT2 and precipitation are associated with the suppression of the moisture transport in the area(Zhang & Villarini, 2019).WT3 exhibits a stronger positive correlation in the western United States due to low atmospheric pressure and strong moisture flux of the area, both of which are the characteristics of this WT(Zhang et al., 2022).WT4 has the opposite features of WT3, showing negative correlation in the western United States(Zhang et al., 2022).On the other hand, the correlation between the WT frequency and temperature shows much clearer spatial patterns (Figure2).These patterns are similar to those of 500-hPa geopotential height (see fig.6inZhang & Villarini, 2019).More specifically, regions with strong positive F I G U R E 3 Maps and boxplots showing the value of the Spearman correlation coefficient between observations and the median of the fitted distribution of the seasonal maximum discharge for each of the four seasons.In the boxplots, the limits of the box represent the 25th and 75th percentiles, while the line inside of it the median; the limits of the whiskers span the 5th and 95th percentiles.

Figure 3
Figure3shows the performance of the seasonal models describing the observed changes in seasonal maximum mean daily discharge with

Figure 6
Figure 6 shows the performance of the Monte Carlo approach in simulating annual maximum discharge.The distribution of the values of the correlation coefficient between observations and the median of the simulated annual maxima across CONUS (Figure 6, top panel) is almost identical to that of four seasonal models (see boxplots in

Figure 3 )
Figure3), indicating that the poor performance of four seasonal models translates into limited skill in describing the interannual variability of annual maximum discharge.We further stratify the results into reference and non-reference sites based on the GAGES-II dataset(Falcone, 2011) to identify the impact of human disturbance on