Study area

The work considered the territory of the state of Nayarit, an entity located in western Mexico. Located in, between the parallels 23° 05’ 04’’ and 20° 36’ 12’’ north latitude and between the meridians of 103° 43’ 15’’ and -105° 45’ 37’’ west longitude (^{INEGI, 2015}).

Meteorological data

Data from the network of agrometeorological stations in Nayarit were used, which consists of automated equipment that collects fifteen minute data on temperature, precipitation, solar radiation and wind (Adcon Telemetry, model A753, Klosterneuburg, Austria). The network operated for eight years since 2007 with 38 stations (Table 1).

Data management

Using the Access 2013 database engine (Microsoft Office 2010, Redmond, Washington, United States), the temperature data organized by weather station, date and time were integrated.

Calculation of accumulated cold hours

For each meteorological station, month and year, cold hours (HF) were quantified. The HF are the records of temperature less than or equal to 12 °C. This temperature threshold was suggested by ^{Norvell & Moore, 1982}. The calculation was made using the following equation:

Where: HFAm are the cold hours accumulated per month and RT are the fifteen minute temperature records less than or equal to 12 ºC.

Annual cold hours data set

For the analysis of the annual data (HFA) the monthly values were averaged for the time series (8 years) for each station. Two databases were obtained, one for the interpolation constituted by the registries of 31 stations and the other with registers of seven stations, representing a sample of 20% for the validation of the interpolation (Table 1).

Cartographic representation

The spatial analysis was carried out in the geographic information system Arcmap Version 10.1 (ArcGIS ESRI, Redlands, California, United States). The interpolation method used for the HFA variable was IDW (Weighted Reverse Distance) and the result of this procedure was classified according to Table 2.

The map of the annual accumulation of cold hours in Nayarit was elaborated in Arcmap Version 10.1, with the spatial statistical method ArcToolBox the state and municipal surface for each class was calculated.

Validation of the interpolation

Accumulated cold hours data resulting from interpolation or predicted data were compared against the observed data from a random sample of seven stations (Table 3). With the statistical program Minitab version 17 (State University of Pennsylvania, United States), the analysis was developed with the linear regression model, calculating the correlation coefficient.

Analysis of the monthly data set. An analysis of descriptive statistics of the daily data organized by month was carried out, with the support of a cash chart elaborated with the statistical program Minitab version 17.

Accumulated annual cold hours of the study area

In Nayarit, 72.6% (2 038 724 ha) of the territory accumulates less than 300 cold hours annually. The remaining 768 549 ha accumulate from 300 to 700 cold hours annually, which according to (^{Norvell and Moore, 1982}; ^{INTAGRI, 2017}; ^{Salgado et al., 2018}) are sufficient for the production of cranberry varieties of ‘Rabbit Eye’ , as well as southern high shrub type Jewel, Misty, Sharpblue, O’Neal, Jubilee or Ozarkblue (Figure 1).

Figure 1 Classification of annual accumulated cold hours in Nayarit.  

The conditions identified between 300-500 HF per year, which represent 18.3% of the state area, may be suitable for the Biloxi variety, which coincides with ^{Salgado et al. (2018)}. The HF demanded by some varieties of cranberry of low and medium cold requirement according to ^{García (2011)} were found in the present work, so in Nayarit it is highly feasible to grow it.

Annual accumulation of cold hours by municipality

In 19 municipalities it was possible to quantify surface area where less than 300 cold hours accumulate annually. The 768 549 ha corresponding to the accumulation of cold greater than 300 annual hours were located in the municipalities of Ahuacatlan, Amatlan de Cañas, Compostela, Del Nayar, Ixtlan del Río, Jala, La Yesca, San Pedro Lagunillas, Santa María del Oro, Tepic and Xalisco. The surface in which they accumulate more than 500 cold annual hours corresponds to the municipalities of Ahuacatlan, Del Nayar, Ixtlan del Río, Jala, La Yesca, San Pedro Lagunillas, Santa María del Oro and Tepic, which represents 256 125 ha, 9.1% of the state territory. Of these, the municipalities of La Yesca and Santa María del Oro stand out with about 180 000 ha (Table 4).

^{García (2011)}, classified the requirements of HF for cranberry in: low (<400), medium (400-600) and high (>800), the previous corresponds to our study to 8.3% and 19.1% of the state surface of the low and medium level respectively.

Spatial distribution of the annual accumulation of cold hours

In Figure 2, it was observed that the region where less than 300 HFA accumulates are distributed throughout the coast, the municipalities from Tepic to Huajicori to the north and in the south, the San Pedro Lagunillas region, the south of Ahuacatlan and Amatlan de Cañas. The region with optimal conditions is concentrated in the center and south of the state, mainly in the municipalities of Santa Maria del Oro, Jala, north of Ixtlan del Río and south of La Yesca.

Figure 2 Spatial distribution of the annual accumulation of cold hours in Nayarit. 

The geographic information system allowed the cartographic representation of climatic data, as well as quantifying the surface of the four classes of annual HF accumulation in Nayarit. The results will allow locating the areas with better conditions for the establishment of crops with specific thermal requirements, such as the cold hours in cranberry, similar investigations were reported by ^{Bhatt et al. (2018)}; ^{Gentilucci et al. (2019)} for kiwi (Actinidia deliciosa) in India and grape for wine (Vitis vinifera) in Italy respectively. On the other hand, ^{Paredes (2010)} points out that cranberry is successfully grown from 600 to 2 500 masl, which is consistent with our results, particularly with the zones with annual accumulation of cold hours >400 that are located at altitudes of 900 to 2 000 m.

Validation of the interpolation model

In Figure 3, the result of relating the data generated by the interpolation of the IDW model (predicted) with the observed ones is shown. In 71.4% of the validation points, interpolation underestimates (residues less than 25 cold hours), even so, the adjustment of the model with a correlation coefficient of 0.97 is very good, only in two validation points the interpolation overestimates with residuals from 9.9 to 16.9%.

Figure 3 Correlation between the values observed and predicted by the interpolation of annual accumulated cold hours.  

The results contrast with that reported by ^{Alzate-Velásquez et al. (2018)}, where they evaluated the IDW interpolation model with an R² of 0.76, in this study the regression model reported better results with 0.97 in R². ^{Yang et al. (2015)} reported results similar to those of the present work, when evaluating the precision of the same interpolation model (R² of 0.94).

Monthly distribution of cold hours

In the region where more than 300 HF is accumulated per year, the largest monthly variation occurs in November and December (with average values >60 HF), being the months when the period of greatest accumulation of HF starts from November to March. In this same period, 50% of the data fluctuates between 40 and 115 HF, indicating a high interannual variability in the region. The lowest accumulation occurred between June and September (average >15 HF), initiating a decline in HF in April (50 average HF) until reaching the lowest accumulation in June with 8.6 HF (Figure 4).

Figure 4 Monthly distribution of cold hours for the region with more than 300 HFA.