A Current Approach to Mean Temperature Trends and Relationships With Teleconnection Patterns in California (U.S.)


 The aim of this research is to expand our knowledge of space-time evolution of mean temperatures at a regional level, for the whole California (United States) over 40 years. This study analyses the relationship between mean temperatures and teleconnection patterns with most influence on the Californian Climate. 170 meteorological stations were used with an observation period that ranged from 1980 to 2019. In order to evaluate the presence or absence of trends, the non-parametric Mann-Kendall test was used. The slope was obtained with a modified Sen’s slope method. The homogeneity of the data from the selected stations was verified. To find out the relationships between temperature and a wide range of teleconnection patterns in California was performed a correlation analysis using the partial non-parametric Spearman Test at a 95% confidence level. Spatial analysis was achieved using Empirical Bayesian Kriging (EBK). During this period, the results show a positive and significant trend annually, monthly and seasonally. Both Pacific Decadal Oscillation (PDO) and West Pacific Oscillation (WPO) are related to temperatures in California State during the period studied.


Introduction.
Global warming is one of the current challenges that human beings have to face due to its negative effects on society, such as oods 1 , heat waves, res and droughts 2 , which are becoming more and more serious over time. The impact produced on ecosystems and on human well-being and health are associated with an increase in average temperatures [3][4][5] . The most signi cant evidence of this Global warming is the increase in air temperature 6 . Global mean surface temperature has risen since the late 19th century 7 . Each of the last four decades has been successively warmer than any decade that preceded it since 1850. The rst two decades of the 21st century However, recent studies suggest that there are slight variations in the maximum and minimum temperatures and these can be easily altered by human activity and land uses at a regional level 10 .
Understanding the trends of climatic variables such as temperature is of great importance both theoretically and in an applied way. From a theoretical point of view, it helps to understand how it has been changing based on previous observations. Moreover, we can establish both the characteristics of this parameter and the trend and use it to project what will happen in the future. Climate is variable in time and space, so detecting a signi cant trend is a great challenge for researchers. To analyse climate data, it is useful to use conceptualizations (mathematical equations) 11 that reduce complexity such as the average temperature. To determine its linear trend, we examine the data values according to when they occurred in the past and then determine a line of t through that data. The gradient of that line will give us the trend.
The calculation of trends in climatic parameters such as average temperature, maximum and minimum temperature has been the subject of a great deal of research in recent years (Cordero et Shrestha et al., 1999) and has been carried out in a wide variety of territories around the world. Most of the studies at this point have focused on large-sale temperature trends. However, it is necessary to carry out more research to focus on the change that occurs at a regional level using the above-mentioned parameters. In this way, researches carried out on decadal trends in average temperatures in various territories of the United States provided impressive results. In this regard, average temperatures across the US have increased from the 1950s to the beginning of the century more than 0,5 ºC. 7,19−26 . In order to study how global warming would affect life at a regional level, models and assessments of climate change often assume that the in uence would be uniform. However, temperatures do not increase uniformly in space or time and few studies have focused on that peculiarity over California State 12,27−29 . The colder hours of the day (nights), the coldest times of the year (winter), and the colder parts of the world (high latitudes) tend to heat up faster. Although, and in contrast to this, in the State of California, temperatures have undergone great variations over the last 100 years, with greater warming being experienced in the southern desert territories 12,30 , where temperatures were regularly high, while in the northern territories the increase has taken place gradually. To be more precise, these temperature increases are uneven for the different regions of the centre and north of the State.
Several climatological research papers have suggested that much of current climate variability observed can be related to variability within a teleconnection pattern 31 . The term teleconnection pattern refers to a large-scale recurring pattern that persists over time with pressure and circulation anomalies that extend to wide geographic areas. In addition, sometimes these patterns can last for several consecutive years. There are some patterns of teleconnection that can directly or indirectly in uence the monthly temperatures of a region of the planet such as the United States 31-37 , or act on a smaller spatial scale such as the State of California 38-43 . Teleconnection patterns that may in uence the United States, including tropical pattern that could affect the southern territories, are Antarctic Oscillation (AAO), Arctic Oscillation (AO), North Atlantic Oscillation (NAO), Paci c-North American Pattern (PNA), Madden Julian Oscillation (MJO), West Paci c Oscillation (WPO) that it is West Paci c (WP), describe by both Barnston and Livezey and Wallace and Gutzler, and the Eastern Paci c (EPO) whereas in the State of California they are mainly El Niño along the Southern Oscillation (ENSO) [44][45][46] and the Paci c Decadal Oscillation (PDO) 28, 47,48 . Although, the effects of teleconnection patterns on California climate variables such as precipitation has been studied before, temperature change and its relationship to teleconnection patterns needs further investigation.
Previous studies have revealed that the climate over California is changing, but how important is the change? Does it occur in a homogeneous way throughout the territory? These are still unsettled questions. With this research it is our intention to help respond these enquiries. There is a lack of current data on temperature trends that account for extreme temperature events in California from 2013 to the present. As far as we know, never before has an investigation been carried out in which the monthly, seasonal and annual values of average temperature trends between the years 1980-2019 for the State of California have been analysed. Furthermore, the aim of this research is to expand our knowledge of space-time evolution of mean temperatures at a regional level, revealing, on the one hand, the trend and its statistical signi cance of the average temperatures for the whole State of California over the last 40 years (1980-2019) at a monthly, seasonal, and annual rate. On the other hand, this study analyses the relationship between mean temperatures and teleconnection patterns with the most in uence on the Californian Climate.
This research is original and shows up-to-date results in average temperature trends in California on a monthly, seasonal and annual time scale. As we have seen in previous studies, they have focused on the correlations of some atmospheric teleconnection patterns with temperatures in short periods of time, for example during a year or in isolated seasonal periods such as in winter. This study shows the possible in uence of up to nine different teleconnection patterns taken all together in consideration on the average temperature in California over 40 years.
Finally, the authors consider that the ndings of this study will help those responsible for land management so that they can take appropriate measures in advance, in the face of Global warming, thus helping them to minimise the effects of this phenomenon.

Study area.
This study is carried out in the State of California, the third largest state in the United States, with an area of 423.955 km 2 . Its orography varies from 84.1 m below sea level in Death Valley to 4418.1 m above sea level on the peak of Mount Whitney 49 . California consists of two major series of mountain ranges: the Coastal Range, the Sierra Nevada, plus the southern tip of the Cascade Range, including Mount Lassen and Mount Shasta. Between these two axes lies the Greater Central Valley, whose Sacramento and San Joaquin river systems drain through Golden Gate (Fig. 1). California's climate is highly variable, and the area ranges from desert to subalpine environments (Pathak et al., 2018). Its complex topography and great latitudinal extension favour a wide variety of climates. Thus, its proximity to the Paci c coast is one of the determining factors in the climate of the state. A Mediterranean climate predominates throughout the state, except for the mountain area of Klamath where there is a temperate climate and the southeast in the Sonoran desert where we nd a tropical climate 27 .

Data.
We chose a wide range of years for this study, a total of four decades (from 1980 to 2019). Three decades are recommended by the World Meteorological Organization (WMO). We took the temperature data from the climatic database of the meteorological stations available on the WRCC website 50 . Monthly average temperature (ºC) data were selected from 350 stations available for California State. 170 of them were nally used for the study (Fig. 1).
The largest number of stations were chosen which covered the maximum surface of the study area 51 . The altitude values and geographic coordinates of each of the stations used were also added to the database to facilitate the representation of the results obtained on maps at a later date. For the statistical treatment of the data, the analysis of the homogeneity of the series was carried out. In this study it was determined by the Run test (Thom, 1966) with a con dence level of 99%. This test is recommended by the World Meteorological Organization (WMO), because it does not require the analysed series to come from a normal sample and it has also been previously used by other climatic studies 14,52 .

Trend analysis.
In order to evaluate the presence or absence of trends we calculate it with the non-parametric Mann-Kendall test, once the homogeneity of the data from the selected stations was veri ed 16,53,54 . The Mann-Kendall test, referred to as the Kendall tau test, is one of the most widely accepted non-parametric tests for detecting trends in time series 51,55−57 . The Sen slope estimator is a non-parametric procedure that estimates changes per unit of time in a series when there is a linear trend.
R package version 4.1.0 was used both to carry out the slope calculations, obtained with a modi ed Sen's slope method and the Mann-Kendall test 58 . All trend analysis was carried out at monthly, seasonal and annual temperature levels. In California, there are 4 seasons: Winter (December, January and February), spring (March, April, and May), summer (June, July, August) and autumn (September, October and November). From now on the months of these seasons will be named as DJF, MAM, JJA and SON respectively. California annual temperature was computed using Voronoi polygons weighting temperature stations by the area of each polygon 59 .
In many regions and areas of the planet it is a challenge to conduct climatic analysis since there are not enough meteorological stations 60 , thus statistical interpolation of the values is necessary for a speci c region. In order to carry out this interpolation, ArcGis 10.8 © 61 software was used and more speci cally an Empirical Bayesian Kriging geoprocessing tool (EBK). It is a method of interpolation of geographic statistics where the standard errors of the prediction are more precise than in other kriging methods 62− 64 . In addition, 17 average temperature trend contour maps were designed with ArcGis 10.8 © and statistically signi cant areas were also superimposed onto the contour maps.

Atmospheric Teleconnection Patterns.
Values of atmospheric circulation pattern indices were taken both from the Climate Prediction Center available on the NOAA National Climatic Data Center (NCDC) website (https://www.ncdc.noaa.gov/teleconnections/) similar to previous research 12,37,48  To nd out the relationships between temperature and teleconnection patterns in California a correlation analysis using the partial non-parametric Spearman Test was performed at a 95% con dence level 58 . This method (the Spearman test) assigns less signi cance to outliers and It is a more robust and resistant alternative for measuring correlation (linear or nonlinear). In addition, this test eliminate the effect that the time variable can exert on the temperature and telepattern variables, in order to avoid ctitious relationships 66 . Finally, all the correlation results and their statistical signi cance are represented in monthly maps. 3. Results And Discussion.

Temperature trends.
The results of the global analysis of temperature in California (Table 1) show that positive trend exist in the whole State. The highest value is found in November (+0.04 ºC year 1 ) and it is statistically signi cant, the same arises with July, August, summer and autumn where the trend reaches +0.03 ºC per year. It is noteworthy that January has shown the same trend (+1.6 ºC) over the period studied such as November but is not statistically signi cant. This results show similarities with other researchers conducted in the State. They have shown that regionally positive temperature trends exist in California but for the northeast region that was proved to be negative 12,28 . The results of analysing temperature trends (positive and negative) at monthly, seasonal and annual average temperature from 1980 to 2019 in the State of California as well as its statistical signi cance at a con dence level of 95% are shown in gure 2.
Positive trends were found each month in more than 60% of the stations. The exception to this is February where 57% of the stations show negative trends. No statistical signi cance was found for negative trends (Fig. 2). Figure 2 revealed that January, June, July, August and November are the months that have shown the highest values of positive statistical signi cance. Although several stations have shown no statistical signi cance, it is notable that when it is positive, there are signi cant trends in nearly half of the stations studied (40%).
According to the monthly results in January the spatial distribution of positive trends was found all over the State, close to 80% of the stations as can be seen in gure 2. This is especially high (+2.25 ºC increase over the period studied) in the Sacramento and San Joaquin Valley (30% of the stations are statistically signi cant).
Autumn 032 ºC year 1 ) and it is statistically signi cant. As we have previously pointed out, this is a rising concern, due to the fact that snowmelt increases in mountain areas probably causing shortage in water supply in the months to come.
If we focus on seasonal trends, it is possible to observe a different seasonal pattern between results. It is especially winter-spring, which is likely to decrease the water supply even further next season 71,80 . In addition, more heat produces more evaporation and so irrigation farmland would need more water, increasing the lack of fresh water even more. All in all, over the period of study as can be seen in gure 2, no negative statistical signi cance was found in California. According to some studies, the increase in temperature is greater in areas of higher agricultural activity, such as the east of the Rocky Mountains, due to the fact that it helps to increase the surface heat capacity and therefore the temperature 81 . Several investigations suggest that these differences in the increase in temperature are affected by several factors; some of them are anthropic activity, land uses and the emission of greenhouse gases 10,82 . Greenhouse gases appear to be related to the increase in average temperatures and the impact derived from this increase 71 . Research on the possible causes of the increase in temperature in the State of California, shows that the existing changes in atmospheric teleconnection patterns have signi cantly altered the extreme temperature events that take place in said region 29 . There is a concrete example in the North Paci c Ocean where surface temperatures correlate highly with Californian temperatures 83 . Finally, a great deal of climatological research suggests that temperature variability can be related to variability within the atmospheric ow 31 .

Teleconnection patterns.
This section shows the results of the spatial and statistical analysis between temperatures and up to nine teleconnection patterns. Table 2 Table 2. This allows us to say that PDO is probably related to increases in average temperatures all over California in the period studied.
According to our results of the PNA pattern in gure 5, appears to be a strong correlation between average temperatures in February. In this month 82% of the stations all over California show the highest statistically signi cant correlation. During the months of June and October this pattern has some in uence throughout the territory studied (30-36% of meteorological stations).
In contrast, WPO has the highest percentage of the stations with statistically signi cant negative correlation with average temperatures. From December to April, negative correlation is observed in the area studied. These values are especially high throughout the territory, in uencing 95.9% of the meteorological stations studied during the month of March and 42.4% during January. Although in this pattern, as we have previously commented, a spatial area of in uence is not observed. We have to take into account that WPO is a temporary pattern and this could explain why it mainly affects the temperatures of winter 38 and spring months in the State of California (Fig. 6, Table 2).
In addition, PDO and PNA are the two teleconnection patterns that present a high percentage of signi cant positive correlation while WPO has the highest negative correlation. These results bear striking similarities with previous investigations undertaken in California in other years 28,31,86 .
If we consider the results regarding the EPO teleconnection pattern (Fig. 7), we can state that it is the one that shows a signi cant positive correlation in November (57.0%) along with PNA and PDO, however, the latter to a lesser extent.
In December, the EPO pattern had no data because there were no values available for the period studied on the data sheet of the Climate Prediction Centre (CPC, NOAA). Searching for alternative values for this pattern in December was not considered in order not to mix diverse information sources. This pattern shows especially high values of positive correlation in April, where 77.9% of the temperature in the stations studied seem to be affected by EPO.
Moving on to NAO correlation results (Fig. 8) (Fig. 9). These results were expected due to the fact that other research highlights the slight correlation with temperature 12,88 .
Contrary to what previous researchers have mentioned, AO (Fig. A1) shows a positive correlation and it is statistically signi cant in the months of March (18.6%), May (26.7%), June (41.3%), July (20.9%), and December (63.4%) ( Table   2). It is important to note that AAO is the pattern that seems to affect average temperatures the least in California (Fig. A2).
The and RMM2. The union of these two gives as a result 8 equatorial phases of this teleconnection pattern. In the light of the results of the correlation of these indexes with average temperature in California, January and November are the months that show the highest positive correlation. To be more precisely, RMM1 (Fig. 10) seems to haven´t got any relation with temperatures over the period studied in California. In contrast, RMM2 (Fig. 11)  On the contrary, Antarctic Oscillation (AAO) and Arctic Oscillation patterns (AO) are unlikely to show any in uence on average temperature trends in California.
The Madden-Julian Oscillation, (RMM2) could play a role in January and November temperatures in the State, due to the fact that in the latter, 41.3% of stations have shown positive correlation.
There is a great variability in the behaviour of the teleconnection patterns in the period studied.
Further investigations on teleconnection patterns and climate variables are essential to establish cause-effect relationships that help us to predict future changes in average temperatures. Knowledge of atmospheric teleconnections provides us with the opportunity to assess interconnection on a planetary scale. Last but not least, this work delves into the up-to-date knowledge of temperature trends in California and also shows their possible relationships with up to nine atmospheric teleconnection patterns. This research could help politicians to make justi ed decisions. Knowing the temperature trends in the state of California and the in uence of teleconnection patterns on them, the policies could mitigate the possible effects caused by global warming. Competing Interests.

Declarations
The authors have no relevant nancial or non-nancial interests to disclose.
Data Availability.
The datasets generated and analysed during the current study are not publicly available due to the fact that R package are waiting to be published but original data source can be consulted in https://wrcc.dri.edu/ and are available from the corresponding author on reasonable request.

Author contributions
Ángel Penas and Sara del Río contributed to the study conception and design. Material preparation, data collection and analysis were performed by Ramón Álvarez Esteban. The rst draft of the manuscript was written by Alejandro González Pérez and all authors commented on previous versions of the manuscript. All authors read and approved the nal manuscript.    Percentage of California meteorology stations with signi cant correlations between WPO and temperature.

Figure 7
Percentage of California meteorology stations with signi cant correlations between EPO and temperature.

Figure 8
Percentage of California meteorology stations with signi cant correlations between NAO and temperature.

Figure 9
Percentage of California meteorology stations with signi cant correlations between ENSO and temperature. Percentage of California meteorology stations with signi cant correlations between RMM2 index of MJO and temperature.

Supplementary Files
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