Study area

The study areas (Figure 1) are the following:

Sitios de muestreo = Sampling sites; Estaciones = Stations.

Figure 1 Geographic location of the sampling sites of Pseudotsuga menziesii (Mirb.) Franco in northern Mexico. 

1) Cerro El Potosí (CPOT), located at 3 670 masl to 15 km from Galeana municipality, south of the state of Nuevo León (24°50'35''-24°53'16'' north; -100°13'12'', -100°15'12"west). The site belongs to the Sierra Madre Oriental, to the sub-province of the Gran Sierra Plegada (Great Folded Sierra), where the average annual rainfall is 400 to 600 mm and the average annual temperature of 12 °C to 18 °C (^{García and González, 1991}).

2) Paraje Puentecillas (PNT), which is located in the area of Santa Bárbara, Pueblo Nuevo municipality, in the south of the state of Durango. The site is located in the limits of El Brillante ejido, coordinates 23º39' north and -105º 25' west. This area has the highest rainfall in the state, around 1 000 to 1 200 mm per year. The average annual temperature is 12 °C, the coldest average of 8 °C and the most extreme of 22 °C (^{Gordon, 1968}; ^{INEGI, 2005}).

3) Sierra de Zapalinamé (SZAP), at the geographic coordinates of 25°15'00"-25°25'58.35" north and -100°47'14.5", -101°05'3.8" west, a system that forms part of the Saltillo and Arteaga municipalities; it is close to the city of Saltillo. The average annual temperature of the area is 18 °C, and the average annual rainfall is 498 mm (^{Meganck et al., 1981}).

Field work

Sampling was carried out selectively with trees ≥ 20 cm DBH in an altitudinal range of 2 500 to 3 100 m. Some criteria for the selection consisted of the specimens having a cylindrical shaft, preferably to avoid problems of release and compression, rooted in shallow soils with long-lived appearance, which is presumed to have more potential to generate dendrochronological series as extensive as possible and with high climatic sensitivity (Constant, 2015). From each selected tree, three radial increments or growth cores (shavings) were taken with a 5 mm-thick Haglöf Sweden Pressler drill.

Laboratory work

The samples were processed through conventional dendrochronological techniques (^{Stokes and Smiley, 1968}) at the Dendrochronology Laboratory of the Centro Nacional de Investigación Disciplinaria Relación Agua, Suelo, Planta, Atmósfera, Instituto Nacional de Investigaciones Forestales Agrícolas y Pecuarias (CENID-RASPA, INIFAP) and in the Laboratory of Carbon Sequestration of the Facultad de Ciencias Forestales de la Universidad Autónoma de Nuevo León (FCF-UANL).

The samples or shavings were mounted with glue in wooden moldings, holding them with adhesive tape to avoid that they twisted during drying and distorted the limits of annual growth due to the effects of moisture loss. Later they were sanding with different grades of sandpaper (300 to 600) and finally they were polished manually to facilitate the observation of growth rings through a high resolution Leica EZ4D stereomicroscope.

Counting of growth rings was made by graphs and tentative dates were assigned to each one (preferable). The measurement of the rings was made with the VELMEX system (0.001 mm), with the software MeasureJ2X for Windows (^{Voortech, 2014}). The measurement data of the growth rings were analyzed with the COFECHA program (^{Holmes, 1983}; ^{Grissino, 2001}), to verify the quality of the date by correlating periods of 50 years with overlap between periods of 25 years (^{Holmes, 1983}).

For the elimination of the noise produced by biological (age) and geometric effects (a growing stems), the series were normalized by means of the ARSTAN program, with a double standardization, which included, in first instance, a negative exponential curve and straight lines of positive or negative regression (^{Cook, 1985}). The values resulting from dividing the measurement value between the resulting value of the curve are known as dendrochronological indices and show an average close to unity and homogeneous variance (^{Fritts, 1976}).

With the ARSTAN program, three versions of the chronology, standard, residual and Arstan were generated; each of them was calculated in a specific way. These series can be used for climate reconstruction purposes, particularly the residual chronology, in which autocorrelation between series has been eliminated (^{Cook, 1985}).

Once the chronologies were obtained for the three study sites, a correlation analysis was performed with precipitation records from climatic stations near to each study site, in order to identify a possible significant relationship between both variables for the purpose of climate reconstruction; thus, the presence of events or periods of drought that will impact the north and other regions of Mexico is determined and it would be possible to argue about the possible causes of such behavior.

To define the period of rainfall that influences the growth of the species, records of climatic stations near the collection sites were used. The stations were chosen from the database of the National Meteorological System, compiled in the program Quick Extractor of Climatological Information (ERIC III) of the Mexican Institute of Water Technology (^{IMTA, 2007}). Stations near the study areas were selected in order to integrate a database of average monthly rainfall at a regional level. The selected climatological stations for the state of Coahuila were: San Antonio de las Alazanas (SMN), San Antonio de las Alazanas (DGE), El Tunal, Jame and Saltillo, for the state of Durango, they were: La Peña, La Ciudad, El Salto 10093, El Salto 10025, Santa Bárbara 2 and Llano Grande and, finally, for the state of Nuevo León, three stations near the study area were identified: 18 de marzo, Mimbres and Galeana.

Data from the selected stations presented information on the monthly rainfall for the period 1954-1999 (46 years) for Coahuila, 1975-2004 (30 years) for Nuevo León and for Durango for the 1963-1985 period (23 years) (Table 1). During these years, a correlation analysis was carried out to detect the months or seasonal period in which there were significant relationships between the dendrochronological time series and the instrumental climate data.

For the generation of the total reconstruction of the period for each study site, a linear regression analysis was made between the standard total ring chronology and the total length of the available climatic data. Due to the short extension of the precipitation data, only the calibration process was performed to generate the reconstruction equation. The verification process had to be carried out on the reconstructed data with information on available dendroclimatic reconstructions previously made for each of the study sites; as well as with records of historical documents of food production, problems of epidemics in humans and social conflicts (^{Endfield and Fernández, 2006}); as well as with reconstructed drought indices for Mexico (^{Stahle et al., 2016}).

To the precipitation reconstructions, a flexible curve (spline) with a rigidity of 67 % was adjusted, which conserves 50 % of the variance, this curve was smoothed at decade level to highlight multi-year events of water scarcity, related to droughts present in the reconstruction.

Similarly, the data of the general chronology was correlated with the Southern Oscillation Index (SOI, for its acronym in English) (^{NOAA, 2016}), since this phenomenon has a high impact on climate variability in northern Mexico (^{Díaz et al., 2002}; ^{Cleaveland et al., 2003}) and with a reconstruction of 1 100 years of standard annual indexes of ENSO (^{Li et al., 2011}; ^{KNMI, 2017}).

Response function

Based on the association between the total ring growth rates and for the previous accumulated monthly precipitation data and during the growing season for each of the sites under study, it was determined that the rainfall period significantly influences (p <0.05) in the growth of the species corresponds to the winter-spring, which involves accumulated rain January-May for PNT and SZAP; for CPOT, the highest correlation was obtained for the January-July seasonal period; that is, its growth is more influenced by the rain that occurs in the cold season of the year while the influence of the summer rain seems to be minimal.

In this study, the relationship between wood and summer precipitation that could have a greater effect on the formation of this growth band was not analyzed. The rain that occurs in the winter-spring period is characterized by being of low intensity and long duration; this allows it not to exceed the infiltration rate and to be retained in the soil matrix to be available at the beginning and during the early stages of growth and early wood formation. In the study areas, the precipitation of the winter-spring interval constitutes around 50 % of the annual total (Figure 3).

Coeficiente de correlación = Correlation coefficient; Mes = Month; Ene = January; Feb = February; Mar = March; Abr = April; May = May; Jun = June; Jul = July; Ago = August; Sep = September; Oct = October; Nov = November; Dic = December.

Figure 3 Correlation coefficient between the ring width index of Pseudotsuga menziesii (Mirb.) Franco in the study areas with the monthly precipitation obtained from climatic stations near the study sites. 

A response of conifers to winter-spring precipitation has been described previously for the Sierra de Arteaga and Cerro El Potosí (^{Villanueva et al., 2010}), and for El Presidio River Basin (^{Díaz-Ramírez et al., 2016}), where positive correlations with early wood growth are described for different seasonal periods of precipitation; that is, January-April, January-May and January-August; although for this study only the total width of the ring was measured, similar results were achieved. On the other hand, the results of PNT and SZAP differ from those reported by ^{Constante et al. (2009)}; ^{Cerano et al. (2012)} who made a reconstruction of the precipitation for the upper part of the Nazas river basin in Durango, and of the southeast of Coahuila, found a positive association between the ring width index and the accumulated monthly precipitation of December of the previous year and January of the current year of growth. In this study, when correlating the total ring width index and the accumulated precipitation, negative coefficients were obtained for the month of December, although PNT showed negative coefficients for November, not for SZAP.

Reconstruction of precipitation

The correlation between observed winter-spring precipitation data and the dendrochronological indexes of the standard version indicated a value of 0.79 for CPOT (n = 27, p <0.001), 0.89 for SZAP (n = 44, p <0.001) and 0.85 for SOP (n = 23, p <0.001); these results are indicative of the high association that both variables have and statistically indicate a good potential to generate a regression model for the purpose of reconstructing precipitation over the length of the chronology with an EPS> 0.85 (Figure 4).

Índice de ancho de anillo = Ring width index; Año = Year; Precipitación = Precipitation.

The upper graph (a) corresponds to the SZAP site (1954-1999 period), the middle one (b) corresponds to CPOT (1975-2004 period) and the lower one (c) to PNT (1963-1985 period).

Figure 4 Behavior of the reconstructed data vs. total ring indexes in its standard version for each of the study sites. 

The models used for the reconstruction included the precipitation records for the periods of 1975-2004 for CPOT, from 1963-1985 for PNT and from 1954-1999 for SZAP. For CPOT, the results indicated r = 0.79 (r² = 0.62, p <0.0001) between the precipitation records and the ring indices. PNT presented r = 0.85 (r² = 0.72, p <0.0001) and finally SZAP, r = 0.89 (r² = 0.79, p <0.0001). The three series explain at least 60 % of the variation in the amount of rainfall that occurs in the winter-spring seasonal period. The regression models for the aforementioned lapses were considered valid in statistical terms for reconstruction purposes (Table 2).

The linear regression models used were the following:

Where:

Yi = Reconstructed precipitation value (mm) for a specific year

Xi = Standardized index for ring width

Detection of dry periods

When applying the linear models, the reconstructed data were generated in the extension of the chronologies with EPS> 0.85. In this way, these data for the CPOT site cover the period 1940-2015 (75 years) (Figure 5), when significant periods of drought were detected, such as those of 1945-1964, 1973-1978, 1995-2003 and 2007- 2014. These results are similar to those of ^{Arreola-Ortiz et al. (2010)} and ^{Canizales (2011)}. This study also detected periods of drought from 1993 to 1998 and from 2008 to 2014, corresponding to the effect of El Niño. In the period from 1945 to 1964, one of the most severe droughts occurred in northern and central Mexico (^{Díaz-Ramírez et al., 2016}), and as a consequence, caused serious unemployment in a large part of the territory, which explains the beginning of the massive migration or bracerism to the United States of America (^{Florescano et al., 1995}).

Precipitación = Precipitation; Año = Year.

The dotted line refers to the average precipitation in the area, the gray color indicates the reconstructed precipitation for the total period of the chronology and, finally, in black, highlights the drought periods at the decade level detected in the reconstruction.

Figure 5 Identification of dry events for CPOT. 

Regarding the PNT site (Figure 6), the reconstructed 1919-2014 period (95 years) indicates important droughts such as those from 1919 to 1924, from 1948 to 1963, from 1969 to 1979, from 1988 to 2001 and from 2008 to 2014. These intervals coincide with those considered by ^{Díaz-Ramírez et al. (2016)} for the Presidio-San Pedro hydrological region, where the authors indicate the presence of intense droughts in the 1920s, 1950s and 1990s. During the period from 1982 to 1983, an intense ENSO event took place, causing droughts for almost the whole country (^{Magaña et al., 1999}), an effect also detected in this reconstruction. Similar periods have been reported by ^{Cerano et al. (2012)} for northern Mexico.

Precipitación = Precipitation; Año = Year.

The dotted line refers to the average precipitation in the area, the gray color indicates the reconstructed precipitation for the total period of the chronology and finally, the soft smoothed line in black highlights the decade-level drought periods detected in the reconstruction.

Figure 6 Identification of periods of drought for the PNT site. 

Finally, for SZAP (Figure 7) the reconstruction extends from 1916 to 2015 (99 years), and it coincides with the dry periods detected in the previous reconstructions, that is, 1916-1919, 1926-1933, 1948-1960, 1970-1980, 1994-2000 and 2008 to 2014. These same periods have been addressed by ^{Villanueva et al. (2011)}, which confirms that one of the most important droughts recorded in northern Mexico occurred during 1950-1965; it is considered the most intense of the 20^th century (^{Stahle et al., 2011}), because it caused severe socioeconomic damages, not only to the population of Durango, but also to neighboring states such as Chihuahua and Coahuila (^{Magaña et al., 1999}), as a result of an intense ENSO event.

Precipitación = Precipitation; Año = Year.

The dotted line refers to the average precipitation in the area, the gray color indicates the reconstructed precipitation for the total period of the chronology and finally, the soft smoothed line in black highlights the decade-level drought periods detected in the reconstruction.

Figure 7 Drought events for the SZAP site. 

Correlation with ENSO

ENSO is one of the circulatory phenomena with the greatest influence on the behavior of climatic variability in northern Mexico (^{Méndez and Magaña, 2010}, ^{Stahle et al., 2016}). In this study, a positive relationship was determined between the ENSO indexes (^{KNMI, 2017}) and tree growth, where the correlations observed were between 0.41 and 0.44 (Figure 8).

The gray line corresponds to the chronology generated for the SZAP site, while the black line corresponds to the chronology of CPOT, and in red that of PNT. The intensity of the ENSO indices is indicated by a smoothed military green line.

Figure 8 Periods of drought influenced by ENSO in northern Mexico. 

According to the Intergovernmental Panel on Climate Change (^{IPCC, 2014}), since 1960 atmospheric phenomena worldwide have been more related to the growth of forest masses at a local level. Likewise, the periods of drought found in the present investigation are related to the ENSO tele-connection, which is significant in northern and central Mexico; For example, the most notorious droughts occurred in the periods 1945-1960, 1969-1979, 1998 and 2011, are related to the influence of this phenomenon.