Historical trends

To validate the estimation of the hourly temperature data, they were adjusted to a linear regression model with real hourly data, resulting in R²= 0.9, complying with the assumptions of 1:1 validation; that is, the intercept was statistically equal to zero and the slope statistically equal to one (^{Fritz et al., 1997}).

With the HF of each of the months of the winter season, historical trends analyze were made from 1961 to 2010 with moving averages every 20 years, considering 1 688 stations (Figure 2). The number of HF in the month of November presents a tendency to decrease (p≤ 0.0001); that is, the average number of HF this month in Mexico has decreased 11.8 h in the 50 years of study, 0.24 h per year (Figure 2A).

The historical trend of the average number of HF in the month of December is on average slightly towards the increase; that is, the number of HF in the 50 years of study has increased 1, 0.02 h per year; however, the model was not significant (p= 0.3718) (Figure 2B). This behavior is due to the fact that in December there was, in general, less accumulation of HF in the period from 1976 to 1995, and then return to normal or slightly greater accumulation of HF (Figure 2B). Figure 2C shows the trend of HF in the month of January, which is towards the decrease (p≤ 0.0001), which has caused a loss of 15.2 HF in 50 years.

Figure 2 Historical trend of the HF number (0 to 7.2 °C). A) November; B) December; C) January; D) February; and E) for accumulated FH from November to February in Mexico. The units of the horizontal axis are years (periods of 20 years) and the units of the vertical axis are number of HF.  

The historical trend of the average number of HF in the month of February is also downward (p≤ 0.0001), with an average decrease of 20.1 HF in 50 years (Figure 2D). Finally, Figure 2E shows the trend of the average number of HF in the winter period from November to February (p≤ 0.0001) and is downward, with an average decrease of 45.3 HF in the period from 1961 to 2010. There is clearly an effect of climate change when presenting the analysis of historical trends in three of the four months and the accumulated winter period a decrease in the number of HF, which has an unfavorable effect on the production of temperate climate fruit trees (^{Medina-García et al., 2011}; ^{Ramírez et al., 2011}).

The analysis of historical trends with the Mann-Kendall test reflected results similar to moving averages. In the four months and the accumulated, the trends were the same, November, January, February and November-February with a negative trend and December with a positive trend, although in all chaos with slightly lower slope values. The significance was the same, except in November where it was not significant with this test (Table 1).

^{Luedeling et al. (2009b)}) found in the Arabian Península decreases in the accumulation of cold (0 to 7.2 °C), in the order of 1.02 to 9.05 h year between 1983 and 2008, in Mexico there was also a decrease in cold, but in the order of 0.91 HF/year in the period 1961-2010, which corresponds to the lower limit of these authors. With this loss trend of 9 HF/decade, in the near future the production of the species that require cold could become marginal or impossible, as indicated by ^{Grageda et al. (2016)} for walnut.

HF estimation models

For the analysis of future climatic scenarios, it is necessary to generate maps with the average number of HF for each month, for this, monthly models were obtained to estimate the HF from the average minimum temperature using the 2 854 stations initially selected. The models that best fit the dispersion of the data (Figure 3), were the logistic models of three parameters. The four models presented values of R²= 0.95 which indicates a very good fit. Table 2 shows the models for the four months.

Figure 3 Scatter plot of the HF data for the month of January and three-parameter logistic model.  

Climatic scenarios

With the models obtained and using the geographic information system Idrisi Selva (^{Eastman, 2012}), national images of HF were generated for the four months of the winter season for the base climate (1961-2010) and for the climates 2030, 2050 and 2070 in each of the 4.5 and 8.5 CPR.

In the Figure 4A shows the maps with the average HF number in the winter period (November to February) in the Mexican Republic. At the moment the fruit trees of temperate climate are cultivated mainly in the zones that have between 600 to 900 HF, according to the map of Figure 4A, the apple tree is cultivated mainly in the zones of 800 to 900 HF, other fruit trees such as peach, plum and apricot are also grown in that same range of HF, but also in areas of 600 to 800 HF.

Figure 4 Average HF number in the winter period (November to February) in the current scenario and in three future climate scenarios of the 4.5 CPR, in the Mexican Republic.  

In the 2030 climate scenario of 4.5 CPR (Figure 4B) the surface of the ranges without cold, 50-200, 200-400 and 400 to 600 HF increases 10.0, 11.5, 5.1 and 12.1%, respectively (Table 3) with respect to the current scenario; that is, the area with less cold accumulation, where temperate climate fruit trees are not grown, is likely to increase, while the surface with greater cold accumulation, where temperate climate fruit trees are grown, shows a decrease in the 600 range -800 HF of 11.7% and in the range of 800-900 HF a decrease of 30.5%.

In the 2050 climate of 4.5 CPR (Figure 4C), the surface of the ranges without cold, 50-200, 200-400 and 400 to 600 HF and the surface with the greatest accumulation of cold (600-800 and 800-900 HF), they present a similar trend to the 2030 climate but more pronounced, so the surface of the 50-200 HF range is likely to increase 29.3% and the area of the 800-900 HF range is likely to decrease 57.1% (Figure 4C and Table 3).

Figure 4D shows the map of the HFs in the 2070 climate of the 4.5 CPR, as in the climates described above, the percentage of the area with less cold accumulation will increase up to 36.4% in the range 50-200 HF while, the percentage of surface area with the greatest accumulation of cold will decrease to 61.6% in the 800-900 HF range (Figure 4D and Table 3).

The areas of high cold accumulation (600-800 and 800-900 HF) will have a strong reduction as the scenarios move forward into the future, especially in areas of the Sierra de Baja California, Sierra Madre Occidental, its adjacent states such as Sonora, Chihuahua, Coahuila, Durango, Zacatecas and Aguascalientes and areas of the Neo Volcanic axis, so it is possible that in those regions a reduction in the suitability of the agricultural surface for temperate fruit trees as indicated by ^{Medina et al. (2011)} in the Chihuahua region of Chihuahua.

The reduction in HF is due to the increase in temperature, which coincides with that indicated by ^{Cavazos et al. (2012)}, in the sense that it will be convenient to use temperate varieties of fruit trees with a lower HF requirement.

Figure 5A shows the maps with the average HF number in the winter period (November to February) in the Mexican Republic. In the 2030 climate of 8.5 CPR (Figure 5B) the surface of the ranges without cold, 50-200, 200-400 and 400 to 600 HF increases 18.8, 27.1, 16.2 and 29.2% (Table 3), respectively, with respect to current scenario; that is, the surface with less cold accumulation, where temperate climate fruit trees are not grown, is likely to increase, while the surface with greater cold accumulation, where most temperate fruit trees are grown, has a decrease in the 600-800 HF range of 26.4% and in the 800-900 HF range a decrease of 68.6%.

Figure 5 Average HF number in the winter period (November to February) in the current scenario and in three future climatic scenarios of the 8.5 CPR, in the Mexican Republic.  

In the 2050 climate of 8.5 CPR (Figure 5C) the surface of the ranges without cold, 50-200, 200-400 and 400 to 600 HF and the surface with greater accumulation of cold (600-800 and 800-900 HF), they present a similar trend to the 2030 climate but more pronounced, so the surface of the 50-200 HF range is likely to increase 40.2% and the surface of the 800-900 HF range is likely to decrease to 94.0% (Figure 4C and Table 3).

Figure 5D shows the map of the HFs in the 2070 climate of 8.5 CPR, as in the climates described above, the percentage of the area with less cold accumulation will increase up to 60.0% in the range 200-400 HF, while, the percentage of surface area with the greatest accumulation of cold will decrease to 99.5% in the 800-900 HF range, it will practically disappear (Figure 5D and Table 3). In this last scenario, practically only in the Sierra Madre Occidental and in some small areas of the neo-volcanic axis it is likely that they accumulate between 600 and 800 HF.

In general, in 4.5 and 8.5 CPR, the same surface reduction and increase behavior is presented in the different ranges of HF, but in 8.5 CPR the increases or decreases are more drastic, this is because this is a scenario of high emissions of GHG; that is, in this scenario there are no policy changes to reduce emissions (^{Van Vuuren et al., 2011}), so with higher GHG emissions there will be greater greenhouse effect and greater temperature increase according to the 8.5 CPR model.

These results are consistent with those found by Baldochi and Wong (2008) in California whereby the year 2100 they expect 500 hours less cold in the winter period. Similarly, ^{Luedeling et al. (2009a)} found similar results for California and for the Arabian Península (^{Luedeling et al., 2009 b}). This author also tested different cold estimation models in California and in all cases, he found a decrease in winter cold (^{Luedeling et al., 2009c}). Similar results were found in Mexico in the Chihuahua area of Chihuahua (^{Medina-García et al., 2011}, ^{Ramírez et al., 2011}) and in peach (^{Ramírez-Legarreta et al., 2008}; ^{Medina-García et al., 2014}).

If the reduction in HF, as observed in all scenarios, is due to the increase in temperature, probable effects on autumn-winter crops will be observed in the future, not only fruit trees with a mild climate, which could even disappear from this cycle in some regions, which would especially affect those species that require some vernalization time, such as wheat, which is one of the main crops in this cycle. It is known that HF lengthen phenological periods by reducing the speed with which physiological processes are carried out and consequently retard growth. Winter wheat will experience a shortening of the sowing-flowering and flowering-physiological maturity stages, in response to the rapid accumulation of heat units (^{Felix et al., 2009}; ^{Zarazúa-Villaseñor et al., 2011a}).

According to the above, it is necessary to initiate research in genetic improvement of annual crops and deciduous fruit trees to adapt to future conditions, because climate change is not a phenomenon that is about to happen, but is already happening, such as it was demonstrated by retrospective climate analysis studies in agricultural areas of the country conducted by ^{Ruiz et al. (2000)}; ^{Zarazúa-Villaseñor et al. (2011a)}; ^{Medina-García et al. (2011)}; ^{Medina-García et al. (2017)}.