Predicting April Precipitation in the Northwestern United States Based on Arctic Stratospheric Ozone and Local Circulation

Using observations and reanalysis, we develop a linear regression model to predict April precipitation in the northwestern United States (PNWUS) with a 1-month lead. Not only does this model reproduce April PNWUS for the training period, but also its predictions are robust and reliable for the independent test period. Two independent factors, Arctic stratospheric ozone (ASO) and geopotential height in western North America at 700 hPa (H700WNA), are used to construct the linear regression model. Based on observations, the possible mechanism by which ASO and H700WNA affect PNWUS is as follows. April circulation anomalies over the North Pacific related to March ASO changes can extend eastward to the western United States, causing April PNWUS anomalies. When the April H700WNA is abnormally high, there will be an anti-cyclonic circulation anomaly over the northwestern United States, which not only inhibits water-vapor transport from the North Pacific to the northwestern United States but also suppresses convective activity. This process also influences the April PNWUS. A transient experiment using a climate model with a longer period also agrees with the above result from observations. Using the predicted April H700WNA from the climate forecast system (CFS) of the National Centers for Environmental Prediction (NCEP) based on March data and the observed March ASO, the April PNWUS predicted by this statistical model is closer to observations than the April PNWUS predicted directly by the CFS using March data.


INTRODUCTION
Precipitation variability throughout the United States has been the subject of recent research, as precipitation above or below normal has the potential to incur significant regional economic and environmental damage (Pielke and Downton, 2000;Andreadis et al., 2005;Manuel, 2008;Seager et al., 2009). Spring precipitation in the United States is not only crucial to agriculture, affecting the sowing and growth of crops, but also affects the natural environment. Excessive spring rainfall can result in nearly saturated soil moisture, causing floods, and mudslides . Thus, the variations and predictability of spring precipitation in the United States are worthy of attention.
Many studies have investigated the factors and mechanisms responsible for spring precipitation in the United States Halpert, 1986, 1987;Trenberth et al., 1988;Trenberth and Branstator, 1992;Trenberth and Guillemot, 1996;Lee et al., 2014;Wang et al., 2015;Steinschneider and Lall, 2016;Li et al., 2018). Wang et al. (2015) analyzed spring precipitation over the southern United States and attributed the precipitation to synergistic effects from an intensified Great Plains lowlevel jet and an anomalous upper tropospheric trough over the southwest United States, which can create a baroclinically unstable environment over the southern United States that is conducive to the maintenance of heavy precipitation (Wang and Chen, 2009;Harding and Snyder, 2015). Subsequently, Li et al. (2018) found that spring precipitation over the southern United States is closely related to the subtropical North Atlantic water cycle. They demonstrated that positive spring precipitation anomalies are associated with an increase in water-vapor fluxes from the subtropical North Atlantic and that their relationship has recently become stronger. In addition, some studies have reported that the El Niño-Southern Oscillation (ENSO), the most significant mode of variation in SST and the atmosphere, is also closely related to spring precipitation in the United States (e.g., Trenberth et al., 1988;Trenberth and Branstator, 1992;Trenberth and Guillemot, 1996). Both the onset and persistence of El Niño can increase spring precipitation in the southern Great Plains and at the same time reduce precipitation in the southeast United States (e.g., Halpert, 1986, 1987;Lee et al., 2014;Wang et al., 2015). Specifically, Lee et al. (2014) found that in the early spring of a decaying El Niño, the atmospheric jet stream and storm track shift southward and that in the late spring of a developing El Niño southwesterly low-level winds shift westward. Zhang et al. (2015) found that ENSO events can affect the upper tropospheric local circulations over North America through exciting Rossby-wave trains. These circulation anomalies cause spring precipitation anomalies in the southern United States and the Ohio Valley. Furthermore, Wang et al. (2015) pointed out that a developing El Niño tends to increase late-spring precipitation in the southern Great Plains and that this effect has intensified since 1980.
Precipitation prediction is the most practical and useful reference for the development of agricultural and economic governance strategy. However, quantitative precipitation forecasting remains one of the greatest challenges in weather forecasting. Currently, most predictions use global circulation models (GCMs), but GCMs are not suitable for surface parameters in specific regions and at sub-grid scales (Risbey and Stone, 1996). To solve this problem, many statistical models have been developed based on physical connections between regional factors and other variables (e.g., Hughes and Guttorp, 1994;Wilby and Wigley, 1997;Goodess and Palutikof, 1998;Salathe, 2003;Hewitson and Crane, 2006;Fowler et al., 2007;Chu et al., 2008;Li and Smith, 2009;Huang et al., 2011;Ruan et al., 2015). For example, Li and Smith (2009) linked the mean sea-level pressure with rainfall over southern Australia during winter and developed a statistical model to predict future regional precipitation. Ruan et al. (2015) successfully developed a model to forecast late-winter precipitation over southwest China based on sea-level pressure in Western Europe and sea-surface temperature in the Western Pacific. Moreover, Li et al. (2016) found that springtime sea-surface salinity over the northwestern portion of the subtropical North Atlantic is closely correlated with summertime precipitation over the United States Midwest. Thus, they regarded springtime seasurface salinity in the subtropical North Atlantic as a predictor of local summertime precipitation. Recently, Wang et al. (2017) proposed a multiple linear regression model based on autumn conditions of sea-ice concentration, stratospheric circulation, and sea-surface temperature that can provide skillful seasonal outlooks of winter precipitation over many regions of Eurasia and eastern North America.
The United States is located in the westerly belt, and the west wind brings considerable water vapor from the Pacific Ocean to the land. The blocking effect of the Rocky Mountains increases precipitation in the northwest United States. Wheat, which is very sensitive to precipitation (Hatfield and Dold, 2018), is the main crop in this area. Therefore, climate change in this region, and particularly precipitation change, is a subject worthy of study. Figure 1A shows correlation coefficients between April precipitation predicted by the climate forecast system (CFS) developed by the National Centers for Environmental Prediction (NCEP) using March data and observed April precipitation from the Global Precipitation Climatology Project (GPCP). Figure 1B shows the standardized time series of April precipitation in the northwestern United States (P NWUS ) based on observation and on CFS prediction, with a correlation coefficient of 0.25. It is found that the CFS has a weak ability to predict April P NWUS with a lead time of 1 month. Therefore, it is necessary to continue to develop methods to predict P NWUS . In addition, tropospheric weather and climate are closely linked to stratospheric processes (e.g., Hu et al., 2019;Zhao et al., 2019;He et al., 2020). Stratospheric signals generated by ozone depletion may propagate down to the troposphere and influence the tropospheric weather significantly (Bai et al., 2015;Hu et al., 2015;Manatsa and Mukwada, 2019;Wang et al., 2019;Zhang et al., 2019), including the tropospheric jet streams (Huang et al., 2017), surface temperature (Zhang et al., 2016Huang et al., 2017;Huang and Tian, 2019), and precipitation (e.g., Luo et al., 2013;Ma et al., 2019). In particular, Ma et al. (2019) revealed that April P NWUS can be modulated by March Arctic stratospheric ozone (ASO). They found that circulation anomalies associated with March ASO variations can propagate to the northwestern United States, leading to local circulation and water-vapor flux anomalies that can affect April P NWUS . This motivates us to investigate whether the March ASO, which has a leading influence on the surface climate in the Northern Hemisphere (Smith and Polvani, 2014;Calvo et al., 2015;Xie et al., 2016Xie et al., , 2017aXie et al., ,b, 2018Ivy et al., 2017;Ma et al., 2019), can be used along with other factors as a predictor of April P NWUS in a statistical model. Results from this new statistical model will be compared with those of the CFS to assess improvements in the predictability of April P NWUS .
In this paper, we develop a linear regression model using the observed March ASO and regional circulation signals to predict the April P NWUS . The remainder of the paper is organized as follows. The data, simulations, and methods used in this study are described in section "Data." The predictors and underlying mechanism are presented in section "Selecting Factors for April P NWUS Predictions." Section "Development of a Linear Regression Model to Predict April P NWUS " describes the linear regression model used for April P NWUS predictions and validates the model using observations and simulations. Results and conclusions are presented in section "Conclusion."

DATA Data
The monthly mean partial ozone column averaged for the latitude of 60 • -90 • N at an altitude of 100-50 hPa after removing the linear trend and seasonal cycle is defined as the ASO index in this paper. The ozone values used in this study are from the Stratospheric Water and OzOne Satellite Homogenized database (SWOOSH, Davis et al., 2016) for 1985-2018. The monthly mean zonal-mean dataset is at 2.5 • × 2.5 • spatial resolution and has 31 vertical levels (316-1 hPa). Xie et al. (2018) showed that the ASO from SWOOSH is in good agreement with that from the Global Ozone Chemistry and Related trace gas Data Records for the Stratosphere (GOZCARDS, 1985(GOZCARDS, -2013 project (Froidevaux et al., 2015), with horizontal resolution of 10 • × 10 • , extending from the surface to 0.1 hPa (25 levels).
Monthly precipitation employed in this study is taken from two sources: the GPCP monthly precipitation dataset provided by the NOAA/OAR/ESRL PSD, Boulder, CO, United States with a horizontal resolution of 2.5 • × 2.5 • (Adler et al., 2003) and the Global Precipitation Climatology Centre (GPCC) with a horizontal resolution of 1.0 • × 1.0 • (Schneider et al., 2008). Geopotential height and winds are obtained from the National Centers for Environmental Prediction-Department of Energy (NCEP-DOE) dataset.
Following Ma et al. (2019) who found that March ASO can significantly influence the April P NWUS , the P NWUS is defined as the area of 39 • -50 • N and 115 • -126 • W in this paper. To understand the characteristics of precipitation in the studied area, Figures 2A,B show the climatology of April P NWUS . It is evident that the spring P NWUS is increasing from the southeast to the northwest and that the primary mode of precipitation variability in this area shows a unified change (Figures 2C,D), indicating that the P NWUS changes can be investigated as a whole. In addition, the April P NWUS exhibits evident interannual changes, and the two sets of precipitation data show a high degree of consistency ( Figure 2E).
The output from the CFS developed by the NCEP is also used in this paper. The CFS is a fully coupled operational dynamical seasonal prediction system (Saha et al., 2006). Its atmospheric component is the NCEP Global Forecast System model used for operational weather forecasting (Moorthi et al., 2001) except at a coarser horizontal resolution. Its oceanic component is the NOAA Geophysical Fluid Dynamics Laboratory Modular Ocean Model V3.0 (Pacanowski and Griffies, 1998). It adopts a spectral triangular truncation of 62 waves (T62) in the horizontal and 64 sigma layers in the vertical. The zonal resolution of the model is 1.0 • , and its meridional resolution is 1/3 • between 10 • S and 10 • N, increasing gradually with latitude before becoming 1 • poleward of 30 • S and 30 • N. We used the monthly data of CFS from 1985 to 2018, including the reforecast  and the forecast period (2011-2018), both of which are a 9-month integration, and we adopted the data starting integration from 00 UTC.

Simulations
The National Center for Atmospheric Research's Community Earth System Model (CESM) version 1.0.6 has been applied in this study to demonstrate the relationship between April P NWUS and the predictors. CESM is a fully coupled global climate model that incorporates interactive atmospheric (CAM/WACCM), ocean (POP2), land (CLM4), and sea ice (CICE) components. The atmospheric component used in this study is the Whole Atmosphere Community Climate Model (WACCM), version 4 (Marsh et al., 2013). WACCM4, as a climate model, has a detailed middle-atmosphere chemistry and a finite-volume dynamical core, extending from the surface to ∼140 km with 66 vertical levels. The interactive chemistry employed in this paper is disabled. The horizontal resolution of the model is 1.9 • × 2.5 • (latitude × longitude) for the atmosphere and approximately the same for the ocean.
We conducted a transient experiment  using CESM incorporating both natural and anthropogenic external forcings, including spectrally resolved solar variability (Lean et al., 2005)

Chemistry-Climate Model Validation (CCMVal) REF-B2
scenario recommendations), a nudged quasi-biennial oscillation (QBO) (the time-series in CESM is based on the observed climatology over the period , and ozone taken from the CMIP5 ensemble mean ozone output. All of the forcing data used in this study can be obtained from the CESM model input data repository.

Holdout Method
The holdout method, sometimes called test sample estimation, relies on a single partitioning of the data. For example, the whole time series is divided into two parts: the period from 1985 to 2007 is the training period, and the period from 2008 to 2018 is the hindcasting period.

Running Holdout Method
This method only differs from the holdout method in its use of a variable-length training period that changes with the hindcasting time point. That is, the required set of regression coefficients and constants are based on the time series before each hindcasting target point. The base period is the shortest training period.

Anomaly Sign Consistency
The anomaly sign consistency (P) is used to compare the observed and fitted April P NWUS (Ruan et al., 2015), as shown in the following equation: where N c represents the number of cases when the observed and fitted P NWUS are both in positive or negative anomalies at the same time, and N represents the sample size.

Root-Mean-Squared Errors
The root-mean-squared errors (RMSEs) proposed in this paper are calculated based on a leave−1−year-out method.  Figure 3C, indicating a significant correlation (95% confidence level) with a correlation coefficient of −0.44 between the two time series. It suggests that March ASO is linked to April P NWUS variations with a lead time of 1 month. This delayed effect can be explained by the process involved in ASO circulation effects; i.e., stratospheric circulation anomalies caused by ASO need a month to propagate to the troposphere in the Northern Hemisphere middle latitudes (Smith and Polvani, 2014;Calvo et al., 2015;Xie et al., 2016;Ivy et al., 2017). Results from the GPCC (Figures 3B,D) agree with those from the GPCP (Figures 3A,C).
As the physical mechanisms linking March ASO and April P NWUS have been explored by Ma et al. (2019) in detail using observations and model verification based on time-slice and transient experiments, here we only briefly describe the physical connection between March ASO and April P NWUS . The correlation coefficients between March ASO and April zonal wind at 200 hPa are shown in Figure 3E. The intensity of April zonal wind over the North Pacific is noticeably affected by variations in March ASO, showing a triple mode with a zonal distribution.

Positive anomaly events (>1 STD)
Negative anomaly events (<-1 STD) March ASO 1999ASO , 2004ASO , 2010ASO 1993ASO , 1995ASO , 1996ASO , 2000ASO , 2005ASO , 2007ASO , 2011 April H700 WNA 1990H700 WNA , 2002H700 WNA , 2004H700 WNA , 2013H700 WNA , 2016H700 WNA 1993H700 WNA , 2003H700 WNA , 2006H700 WNA , 2010H700 WNA , 2012H700 WNA , 2017 This means that when March ASO increases, zonal wind in the higher and lower latitudes of the North Pacific displays a positive anomaly, whereas zonal wind in the mid-latitude North Pacific demonstrates a negative anomaly ( Figure 3E). These circulation anomalies can extend eastward to the western United States, influencing regional circulation and climate Ma et al., 2019). Specific wind anomalies related to March ASO variations in the troposphere are shown in Figure 3F. Wind anomalies in the northwestern United States are dominated by the northeast wind when the March ASO is abnormally high. These conditions suppress local precipitation. Opposite results are found when March ASO is abnormally low. Given this relationship between March ASO and April P NWUS , we select March ASO as the first factor in our model for predicting P NWUS . The correlation coefficients in Figure 3 suggest that the ASO only partially explains variations in P NWUS . Therefore, other factors that affect P NWUS must be identified. First, we divide the variations of P NWUS into two parts: the ASOrelated part (P NWUS_ASO ) and the remainder (P NWUS _ NOASO ). The P NWUS_ASO is obtained by regressing P NWUS variations onto ASO, and P NWUS _ NOASO = P NWUS -P NWUS_ASO . P NWUS_NOASO describes P NWUS variations with the effects of ASO removed.
To simplify the problem, we investigate the circulation factors that directly affect precipitation. To find a factor for P NWUS _ NOASO , correlation coefficients between April P NWUS _ NOASO variations and simultaneous geopotential height anomalies (after removing the signals of March ASO from the geopotential height) at 200, 500, and 700 hPa are shown in Figure 4. There are 17 regions with significant correlation identified in Figure 4. The circulation anomalies in these regions may be factors involved in the remaining precipitation (P NWUS _ NOASO ) variations. RMSEs are calculated for each potential factor to find the best factor in the model. The three factors with the smallest RMSE are shown in the row labeled "Step 1" in Table 2. The factor H700 WNA (geopotential height in western North America at 700 hPa) has the lowest RMSE (14.09 mm), and the correlation coefficient between this factor and P NWUS _ NOASO is the largest and is significant at the 95% confidence level. This factor also passes the T and F tests. Therefore, April H700 WNA is provisionally selected as the second factor in the model for predicting P NWUS .
Next, we discuss the physical processes involved in the effects of April H700 WNA on simultaneous P NWUS _ NOASO . Figure 5A shows climatological values for April wind, which indicate that the northwestern United States is dominated by the west wind. Figure 5B presents differences in composite April wind between positive and negative April H700 WNA anomaly events at 700 hPa. Circulation anomalies related to April H700 WNA are anti-cyclonic in western North America when April H700 WNA is abnormally high. This corresponds to a divergence of the airflow, which is unfavorable for water-vapor transport from the North Pacific to this area and strengthens dry, cold air transport from the north. Because anti-cyclonic circulation tends to suppress convective activity, a pressure-longitude crosssection of the differences in composite April vertical-longitude wind between positive and negative H700 WNA anomaly events is shown in Figure 5C. The northwestern United States is R represents the correlation coefficients between potential forcing factors and April P NWS . *Significant at the 95% level. **Significant at the 99% level.  Table 1 for specific April H700 WNA anomaly events.
covered by an anomalous downwelling airflow during positive H700 WNA events, suppressing convective activity. This less watervapor and downwelling airflow anomaly results in a decrease in April P NWUS during positive H700 WNA anomaly events, with the opposite occurring during negative H700 WNA anomaly events.
The above analysis demonstrates that circulation anomalies (H700 WNA anomalies) can modulate simultaneous P NWUS _ NOASO and supports our selection of H700 WNA as a factor in the statistical model. Other factors contributing to P NWUS _ NOASO are investigated next. First, we divide the variations of P NWUS _ NOASO into two parts: the H700 WNArelated part (P NWUS _ NOASO _ H 700 ) and the remainder (P NWUS _ NOASO _ NOH 700 ). P NWUS _ NOASO _ H 700 is obtained by regressing P NWUS _ NOASO variations onto H700 WNA , and P NWUS _ NOASO _ NOH 700 = P NWUS _ NOASO -P NWUS _ NOASO _ H 700 . P NWUS_NOASO_NOH 700 describes P NWUS variations with the effects of ASO and H700 WNA removed. Figure 6 shows the correlation coefficients between April P NWUS_NOASO_NOH 700 and simultaneous geopotential height anomalies (after removing the signals of March ASO and April H700 WNA from the geopotential height). Thirty-two potential factors are identified. The three factors with the smallest RMSE are shown in the row labeled "Step 2" in Table 2. The factor with the lowest RMSE is the geopotential field located in the North Pacific at 700 hPa. Although the correlation coefficient between this factor and P NWUS_NOASO_NOH 700 is significant at the 95% confidence level, it passes neither the t-test nor the F-test. This suggests that, in terms of the circulation field, there are no remaining factors that can explain variations of P NWUS_NOASO_NOH 700 better. Thus, only ASO and H700 WNA are selected as predictors in the model, and no additional factors are investigated.

DEVELOPMENT OF A LINEAR REGRESSION MODEL TO PREDICT APRIL P NWUS
Local precipitation may be affected by both linear and nonlinear climate forcing factors. However, Zorita and Von Storch (1999) pointed out that linear models offer a clearer physical interpretation. Guo et al. (2012) indicated that linear models perform well on monthly mean seasonal time scales. Thus, we construct a linear regression model to predict April P NWUS . Two factors, March ASO and April H700 WNA , are selected for use in the model.
The ASO leads P NWUS variations by about 1 month and can thus be considered as a predictor. However, the H700 WNA and P NWUS correlation is simultaneous (April), so April H700 WNA cannot be used in a statistical model for predicting April P NWUS . A B C FIGURE 6 | Correlation coefficients between April P NWUS_NOASO_NOH700 and simultaneous geopotential height at (A) 200, (B) 500, and (C) 700 hPa during 1985-2018. The ASO and H700 WNA signals were removed from the geopotential height before calculating the correlation coefficient. Boxes are the regions of the potential factors. Shaded areas indicate statistically significant correlation at (at least) the 90, 95, and 99% confidence levels.
The CFS developed by NCEP is suitable for evaluating circulation variations in the northwestern United States; i.e., April H700 WNA predicted by the CFS using March data is significantly correlated (95% confidence level) with April H700 WNA from NCEP2 with a correlation coefficient of 0.33 ( Figure 7A). Thus, we use observed March ASO and April H700 WNA predicted by the CFS using March data as the two predictors in the linear regression model. Note from the standardized time series of the two predictors ( Figure 7B) that they undergo significant interannual variations and are independent of each other (r = 0.02, not significant at the 95% confidence level).
According to the holdout method, we use these two predictors and P NWUS to establish a linear regression model for the training period   where the units of April P NWUS , March ASO, and April H700 WNA are mm, DU, and m, respectively.
The time series of observed, fitted, and predicted P NWUS according to the above linear regression model are shown in Figure 8A. During the training period , the correlation coefficient and anomaly sign consistency rate between the observed and fitted P NWUS are 0.44 (significant at the 95% confidence level) and 48%, respectively. During the test period (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018), these values between the observed and predicted P NWUS are 0.50 (significant at the 90% confidence level) and 46%, which are similar to the values during the training period. To further examine the stability and predictability of the linear regression model, we re-predict April P NWUS during the test period (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018) using the running holdout model (see section "Data") -i.e., we train the linear regression model on a different period. The results are shown in Figure 8B. During the test period (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018), the correlation coefficient and anomaly sign consistency rate between the observed and predicted P NWUS are 0.53 (significant at the 90% confidence level) and 46%, respectively. This is consistent with the results shown in Figure 8A, indicating that the linear regression model is stable and reliable.
To further test the robustness of the linear regression model with a longer time series, a transient experiment is implemented next. Details of the model and experiment are provided in section "Data." The results are shown in Figure 9. Significant correlations are found between the CESM-simulated and fitted April P NWUS during the training period with a correlation coefficient of 0.63 (significant at the 99% confidence level) and between the  CESM-simulated and predicted April P NWUS with a correlation coefficient of 0.75 (significant at the 99% confidence level) during the test period. The transient experiment illustrates that a strong connection exists among March ASO, April H700 WNA , and April P NWUS and that the linear regression model is stable and reliable, supporting the results from observations described above.
Note that the magnitude of the fitted and predicted precipitation variations is larger than that in the observations (Figure 8). This may be because the April H700 WNA predicted by the CFS using March data is smaller than that observed ( Figure 7A). To address this issue, we correct the April H700 WNA A B FIGURE 10 | (A) Is the same as Figure 7A and (B) is the same as Figure 8A, except that the CFS-predicted April H700 WNA using March data has been corrected by adding a constant value of 19.26.
predicted by the CFS using March data by adding a constant value of 19.26 ( Figure 10A, the difference between the average of observed April H700 WNA and April H700 WNA predicted by the CFS in March for the period 1985-2018). Then, we use March ASO and the corrected April H700 WNA to build the linear regression model for predicting April P NWUS . The new model is shown as follows: The results shown in Figure 10B are similar to those shown in Figure 8A. Note that the magnitude of the fitted and predicted precipitation variations is closer to that of observations. This suggests that the agreement of the predicted P NWUS with observations was improved.
In addition, the correlation coefficients among observed P NWUS , ASO, H700 WNA , and fitted P NWUS variations are also significant at the 95% confidence level based on the Monte Carlo test (not shown), which supports the conclusions based on the Student's t-test.

CONCLUSION
The March ASO can be used as a predictor for April P NWUS because its anomalies significantly influence April tropospheric winds over the North Pacific with a triple mode. Circulation anomalies can extend eastward to western North America, causing wind anomalies in the northwestern United States in the troposphere. For example, the northwestern United States is dominated by northeast wind anomalies when there is an increase in March ASO. These conditions weaken local precipitation. When the April H700 WNA is abnormally high, circulation anomalies are anti-cyclonic in the western United States, which is unfavorable for water-vapor transport from the North Pacific to this region. Furthermore, the northwestern United States is covered by an anomalous downwelling airflow suppressing convective activity. This leads to less P NWUS .
Based on observed March ASO and April H700 WNA predicted by the CFS using March data, we developed a linear regression model to predict the April P NWUS with a 1-month lead. Results show that the linear regression model not only reproduces the historical April P NWUS during the training period, but its predictions are also robust and reliable for the independent test period. Results from WACCM4 also support conclusions drawn from the analysis of observations. Finally, we compare the April P NWUS directly predicted by the CFS using March data to that predicted by the statistical model in March described here. The correlation coefficient between the observed April P NWUS and that predicted by the CFS using March data is 0.25 during 2012-2018 (before 2011, no CFS-predicted April P NWUS data are available), whereas the correlation coefficient between the observed April P NWUS and that predicted by the linear regression model is 0.53. This indicates that, at this stage, the linear regression model is better able to predict April P NWUS than CFS at a lead time of 1 month. In summary, the linear regression model described here can be used to improve predictions of April P NWUS variations.

DATA AVAILABILITY STATEMENT
The datasets generated for this study are available on request to the corresponding author.

AUTHOR CONTRIBUTIONS
XM and FX designed the study, contributed to the data analysis and interpretation, and manuscript writing.

ACKNOWLEDGMENTS
We acknowledge the ozone datasets from the SWOOSH, precipitation data from the GPCC, GPCP, and CFS, and meteorological fields from NCEP2. We thank NCAR for providing the CESM model. This research was supported by Super Computing Center of Beijing Normal University, user name is xiefei.