As aforementioned, Mexico is generally characterized by dry climates. But, the southern part of Mexico is relatively wet due to seasonal invasion of the Intertropical Convergent Zone (ITCZ). The northern and northwestern parts of Mexico are dominated by a high pressure system nearly throughout a year, resulting in a dry climate with the mean annual precipitation being less than 500 mm. Furthermore, nearly 70% of the rainfall falls between June and September, further exacerbating the problems related to water-resource availability and also to water-resource reallocation (CONAGUA, 2014).

The area devoted to agriculture in Mexico is approximately 21× 10⁶ hm², 31%(i.e., 6.5× 10⁶ hm²) of which is irrigated and 69% (i.e., 14.5× 10⁶ hm²) of which is rain fed (CONAGUA, 2014). Agriculture plays an important role in the economic development of the country, accounting for 8.4% of the gross domestic product and employing 23% of the economically active population. Irrigated agriculture contributes approximately 50% of the total value of agricultural production.

Again, drought has been an inevitable natural disaster throughout Mexican history. A recent three-year (2010-2012) drought in Mexico has resulted in $1.5× 10⁹of economic damages, the damages include loss of 450× 103 heads of cattle, and reduction in crop yields. The immediate consequence of these damages was the rising price of agricultural products, predominantly affecting the poorest sector of the society. It should be particularly noted that the greatest damage occurred in the northern and northwestern parts.

The states situated in northern and northwestern parts of Mexico include Aguascalientes, Baja California, Baja California Sur, Coahuila, Chihuahua, Durango, Nuevo Leó n, San Luis Potosí , Sinaloa, Sonora, Tamaulipas, and Zacatecas (Fig. 1). These states cover a surface area of 1, 193, 134 km² and they had a total population of 32, 281, 464 in 2015 (INEGI, 2015), being27% of the national total. It should be stressed that this region (i.e., studied area) is the one that the most severe droughts have occurred (Esparza, 2014). Topographically, the region is composed of a central plateau, two mountain ranges and a coast plain. The two mountain ranges, the Sierra Madre Occidental and the Sierra Madre Oriental, are separated by the central plateau and the coastal plain separates the Sierra Madre Oriental from the Atlantic Ocean. Climatologically, the northern and northwestern parts of Mexico (i.e., studied area)are predominantly arid and semi-arid climates, covering77% of the region’ s territory and consequently the states in northern and northwestern parts of Mexico are under water stress of varying degrees (Table 1).

Fig. 1

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	Fig. 1 Thestudy area (shadow regions) and map of Mexico

Table 1

Table 1

Table 1 Water stress distribution in northern and northwestern parts of Mexico State Population Water use (hm³ ) Average water availability (hm³ ) Water stress (%) Aguascalientes 1, 312, 544 617 1051 59 Baja California 3, 315, 766 3001 2495 120 Baja California Sur 712, 029 411 2505 16 Coahuila 2, 954, 915 1960 5308 37 Chihuahua 3, 556, 574 5065 12, 493 41 Durango 1, 754, 754 1536 11, 686 13 Nuevo Leó n 5, 119, 504 2051 2478 83 San Luis Potosí 2, 717, 820 1383 7384 19 Sinaloa 2, 966, 321 9173 9788 94 Sonora 2, 850, 330 7519 7290 103 Tamaulipas 3, 441, 698 3885 13, 586 29 Zacatecas 1, 579, 209 1484 7025 21 Northern Mexico 32, 281, 464 38, 085 83, 088 46

Table 1 Water stress distribution in northern and northwestern parts of Mexico

According to Sirdas and Sen (2003), the annual time series method issuitable forassessing long-term drought features. This study thus adopted the method to assess long-term drought features based on the annual precipitation data of64 years spanning from 1950 to 2013obtained from 649 meteorological stations situated within the study area (Fig. 2). The only criterion for a meteorological station to be considered was that its recording period has to cover at least 85% of the total period of 64 years. In the present study, a feed-forward artificial neural network approach, similar to that proposed by Teegavarapu and Chandramouli (2005), was chosen for interpolation of missing rainfall data.

Fig. 2

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	Fig. 2 Locations of the meteorological stations selected for this study

The theory of runs proposed by Yevjevich (1967) was used to obtain the meteorological drought features for each time series (Fig. 3). A negative run, d* , occurs when the precipitation, X_t, is consecutively less than X₀ during one or more time intervals (years). Similarly, a positive run occurs when X_t is consecutively greater than X₀. We focused only on negative runs because they are relatedto drought features. A run can be determined by its duration D(years), and its severity (S)or the accumulated deficit is the sum of the differences between the threshold and the precipitation in the time (in mm). The drought intensity I=S/D(in mm/a). The time span between two runs is known as drought periodicity, P.For this study, an additional drought feature was estimated, i.e., the available rainfall in an average drought period, which is actually the difference between the threshold and the average run severity.

Fig. 3

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	Fig. 3 Meteorological drought properties defined for a threshold X0 (7th and 10th runs)

To obtain the long-term meteorological annual drought features, we generated10× 10³synthetic monthly samples for each rainfall series. The periodic autoregressive moving average (PARMA) model was used for this purpose (Salas et al., 1988):

Y_{ν , τ} = Σ ϕ _{1, τ} Y_{ν , τ -i}  ε _{ν , τ} -Σ θ _{1, τ} ε _{ν , τ -j.}(1)

Where Y_{ν , τ} represents the precipitation process for year ν and season τ . For each seasonτ , this process is normally distributed with a mean of zero and varianceσ _τ ²Y). ε _{ν , τ} is the uncorrelated noise term which is normally distributed for each season with a mean of zero and varianceσ _τ ²Y).{ϕ _{1, τ} , . . ., ϕ _{p, τ} } includes the periodic autoregressive parameters and{θ _{1, τ} , . . ., θ _{p, τ} } includes the periodic moving average parameters. Although this model has a limited ability to capture non-stationarity and non-linearity in data, it has been generally accepted by practitioners.

In Mexico, the “ National Institute of Ecology and Climate Change” performed a regional climatic analysis using projections from 15 global circulation models(Table 2) of the Coupled Model Intercomparison Project Phase 5 (CMIP5) under the prevailing conditions of the RCP 4.5, RCP 6.0 and RCP 8.5 scenarios forthe near future (2015-2039) and also for the far future(2075-2099). Each model employed a grid between latitudes 5.25° N and 34.75° N and longitudes 74.75° W and 121.25° W. The annual anomalies of the four output variables (precipitation, maximum, minimum and average temperature) for each RCP scenario were presented in a 0.5° × 0.5° grid (INECC, 2014).

Table 2

Table 2

Table 2 Coupled Model Intercomparison Project Phase 5 global circulation models 1Max Plank Institute(MPI-ESM-LR) 6Beijing Climate Centre (BCC-CSM1-1) 11Atmosphere and Ocean Research Institute (MIROC5) 2Institute for Numerical Mathematics (INM) 7Institute Pierre-Simon Laplace (IPSL-cm5a-Ir) 12Met Office Hadley (MOHC) 3Norwegian Climate Centre (NorESM1) 8NASA Goddard Institute for Space Studies (GISS-E2-R) 13Meteorological Research Institute(MRI-CGCM3) 4Canadian Centre for Climate Modelling and Analysis (CanESM2) 9, 10Japan Agency for Marine-Earth Science and Technology (MIROC.-esm-chem) 14Geophysical Fluid Dynamics Laboratory (GFDL-CM3) 5Centre National de Recherches Meteorologiques (CNRM-CM5) 10Japan Agency for Marine-Earth Science and Technology (MIROC-esm) 15Australian Commonwealth Scientific and Industrial Research Organization (CSIRO-MK3-6)

Table 2 Coupled Model Intercomparison Project Phase 5 global circulation models

This study analyzed the responses of the meteorological drought features in northern and northwestern parts of Mexico to the IPCC-prescribed RCP 4.5 scenario (i.e., a pre-2100 emission stabilization scenario) for the near future (2015-2039) and also to the IPCC-prescribed RCP8.5 scenario (i.e., a very high baseline emission scenario) for the far future (2075-2099).

Spatial analysis of the mean annual precipitation(MAP) allows us distinguish the “ dry areas” from the “ wet areas” (Fig. 4). The “ dry areas” include the entire Baja California Peninsula (MAP≤ 400 mm), the Sonora (MAP≤ 375 mm), and the central plateau (MAP≤ 250 mm). The “ wet areas” are situated in the eastern part of the region, including the states of San Luis Potosí , Tamaulipas, the south-eastern zone of Nuevo Leó n, and also some regions in the states of Sinaloa, Chihuahua and Durango. Due to orographic effect, the mean annual precipitation (MAP) in the highlands of the eastern mountain ranges (i.e., Sierra Madre Oriental) reaches a value of 1350 mm.

Fig. 4

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	Fig. 4 Spatial distribution of the mean annual precipitation (mm) in northern and northwestern Mexico based on the available data (1950-2013)

The long-term drought features under normal conditions (the average between 1950 and 2013) were estimated from 10× 10³ synthetic samples generated from the mean annual precipitation data of all selectedmeteorological stations. The results reveal that the region suffered a drought on average every 4.1 years with a mean duration of 2.2 years and with an intensity of 143 mm/a (24.2% belowthe average).The mean annualprecipitation in drought episodes is only 447 mm (Fig. 5), whereas themean annual precipitationduring the data-available period (1950-2013) is 590 mm (Fig. 4).

Drought duration throughout the region varied from 2.0 to 2.8 years. The intensity of drought also varied across the region. The driest places (e.g., the California Desert) experienced droughts withintensities ranging from 35% to 50% below the average and less dry places (e.g., the Sonoran Desert and central plateau) experienced droughts with intensities varying from 25% to 35% below the average. The intensity was considerably lower in the mountain ranges (15% to 25% below the average) and also in the southern part (i.e., Zacatecas and Aguascalientes) of the studied area (10% to 20% below the average).

Fig. 5

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	Fig. 5 Spatial distribution of the mean annual precipitation (mm) in northern and northwestern Mexico under drought episodes occurred during the data-available period (1950-2013)

The RCP 4.5 (2015-2039) scenario-simulation resultsindicate that the region would suffer from a drought every 4.3 years in the near future (2015-2039) with an average duration of 2.7 years and with an intensity of 165 mm/a (28% below the average) and that the regional mean annualprecipitationwould be only425 mm (Fig. 6). The RCP 8.5 (2075-2099) scenario-simulation resultsindicate that the region would suffer from a drought every4.7 years in the far future (2075-2099) with an average duration of3.2 years and with an intensity of 182 mm/a (30.8% below the average) and thatthe regional mean annualprecipitationwould be only408 mm (Fig. 7).

Fig. 6

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	Fig. 6 Spatial distribution of the mean annual precipitation (mm) in northern and northwestern Mexico during droughts for the RCP 4.5(2015-2039) scenario

In the RCP 4.5 (2015-2039) scenario, the projected drought duration would continue to be spatially homogeneous acrossthe region, varying from 2.5 to 3.0 years. The longest drought durations would occur in central Sonora and Baja California, ranging from 3.0 to 3.5 years.In the RCP 8.5 (2075-2099) scenario, the projected drought duration would vary from 3.0 to 3.5 yearsin the eastern part(i.e., Nuevo Leó n, San Luis Potosí , Tamaulipas and eastern Coahuila and Zacatecas) and from 2.5 to 3.0 yearsin the central part (i.e., Durango, eastern Chihuahua and western Coahuila). The drought durations would be up to 4 years in southernZacatecas and up to 5 yearsin central Sonora. The duration would vary from 2.5 to 3.0 years in the remaining areas (e.g., the Baja California Peninsula).

Fig. 7

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	Fig. 7 Spatial distribution of the mean annual precipitation (mm) in northern and northwestern Mexico during droughts for the RCP 8.5(2075-2099) scenario

The spatial distribution of the intensity under different scenarios would follow the same pattern as under normal conditions and the presently driest places would have the most intense droughts. The California Desert would experience droughts with an intensity ranging from 47% to 57% below the average. Similarly, the Sonoran Desert and central plateau would experience drought with intensities ranging from 30% to 45%. In the highlands of the mountain ranges the intensity would vary between 20% and 30% below the average, and in the southern tip of the region the intensity would be approximately 15% below the average.

4.1Expectedwater stress

Due to the naturally arid conditions in northern and northwestern Mexico, the water resources in the region are already stressed under the current socioeconomic status (see Table 1), and the continuation of the rapid population growth would definitely aggravate the water stress level(CONAPO, 2015). Magañ a-Rueda (2006) suggested that the water stress levels would further increase by7%-17% above the current levels for northern and northwestern Mexico in the year 2030, considering water-demanding factors includingpopulation, gross domestic product, water and food demand and other factors. Furthermore, if the RCP 4.5 scenarios for the near future (2015-2039) and the projectedpopulationfor the year 2030 are taken into consideration (CONAPO, 2015), the water stress levels would become much worse and the water stress levels for the studied area would further increase by nearly 30% above the current levels (Table 3).

Table 3

Table 3

Table 3 Water stress in northern and northwestern Mexico under drought conditions for the RCP 4.5(2015-2039) scenario State Population (2030) Water use (hm³ ) Average water availability in drought (hm3) Water stress (%) Aguascalientes 1, 403, 549 730.94 460.7 158.65 Baja California 3, 838, 573 3652.01 1953.6 186.94 Baja California Sur 935, 908 603.37 1732.0 34.84 Coahuila 3, 203, 950 2284.68 3192.8 71.56 Chihuahua 3, 955, 472 5880.78 8830.2 66.60 Durango 1, 880, 903 1769.12 8300.8 21.31 Nuevo Leó n 5, 604, 167 2470.19 2739.7 90.16 San Luis Potosí 2, 914, 568 1558.81 6391.1 24.39 Sinaloa 3, 154, 280 10, 454.24 7236.3 144.47 Sonora 3, 213, 165 9074.49 5686.0 159.59 Tamaulipas 3, 818, 219 4538.79 7950.9 57.09 Zacatecas 1, 656, 459 1649.53 4737.6 34.82 Northern Mexico 35, 579, 213 44, 666.95 59, 211.8 75.44

Table 3 Water stress in northern and northwestern Mexico under drought conditions for the RCP 4.5(2015-2039) scenario

A lack of rainfall mainly affects the crops of rain-fed agriculture. The rain-fed agriculture is 2-fold greater than that of irrigated agriculture in terms of areal extentsin northern and northwesternMexico (SIAP, 2015). In the most recent drought year (i.e., 2011), rain-fed bean production(224× 10³ tons) and rain-fed maize production (505× 10³tons) were considerably lower than expected, and the drought-resulted economic loss was as high as $363 million. The most affected states were Zacatecas, San Luis Potosí and Durango and the losses amounted for79% of the total losses in the region (SIAP, 2015). In the same year, some states, such as Baja California Sur and Zacatecas, did not sufferfrom the drought, but the groundwater extractions for irrigation were 54% and 40% higher than the averages between2006and2010(INEGI, 2015). During the period from 1980 to 2013, the average annual rain-fed agricultural lands were2, 428, 245hm²in total and theaverage annual drought-damaged agricultural landsaccountedfor 19% of the total (SIAP, 2015). To estimate the drought-damaged percentages of the rain-fed agricultural landsduring the data-available period (1950-2013) for each state, we established a statistical relationship between the damaged percentages of agricultural lands and the mean annual precipitation amounts. Our estimates suggest that the mean annual precipitation(MAP) during a drought episode is416 mm and the possible damaged percentages of rain-fed agricultural lands reaches56% under current conditions (i.e., 1950-2013) in Aguascalientes. The damaged percentage increases to 60% in the near future (2015-2039) for the RCP 4.5 scenario and up to 65% in the far future (2075-2099) for the RCP 8.5 scenario. Table 4 presents the expected percentage of the damaged agricultural lands for the remaining states in the central plateau and Baja California Peninsula. It should be noted that Baja California Sur is an exception because no rain-fed agriculture is practiced there.

Table 4

Table 4

Table 4 Expected percentage of damaged rain-fed agricultural lands under drought conditions for different climate scenarios State Average area of annual sowing of rain-fed land (hm2) Current condition (1950-2013) (%) RCP 4.5 (2015-2039) (%) RCP 8.5 (2075-2099) (%) Baja California 35, 909 54 59 60 Chihuahua 654, 890 27 29 30 Coahuila 54, 055 28 29 30 Durango 523, 051 18 21 23 Zacatecas 1, 059, 254 21 24 29

Table 4 Expected percentage of damaged rain-fed agricultural lands under drought conditions for different climate scenarios