Phases of research, input and pre-diagnosis information

The research was carried out in three phases, with a trans-scalar approach (from regional to local), as described by ^{Segundo and Bocco (2012)}. Thus, a SU reference pre-diagnostic was established. The general characteristics of the phases were as follows.

Phase I. Preliminary data and research of the SU agricultural process. The input information included the vector sets (shp) at scale 1: 250,000 of the Soil Science Series II (^{INEGI, 2007}) and Land Use and Vegetation (USV) series V (^{INEGI, 2010}). From the USV vector set we obtained the polygons of dryland agricultural use (Figure 1a and 1b); while the agricultural process in the SU was documented with support from the reporting producers.

Phase II. The information from Phase I was analyzed and interpreted by contrasting it with information of higher resolution. To this end, the vector sets of the ejido coverage were used at a 1: 50 000 scale; the digital elevation model with resolution of 30 m, which was downloaded from the Mexican Elevation Continuum (Continuo de Elevación Mexicana) (CEM 3.0) of ^{INEGI (2015)} and the scene (Path/Row) 30/42 from LandSat May 8, 2014, downloaded from the United States Geological Service Portal (^{USGS, 2015}). From the latter, we obtained sub-images consistent with the SU coverage in order to identify areas of agricultural use (Figure 3a and 3b).

Phase III. In this phase, we identified the requirements for field work, such as the technical profile of expert observers (EO) and the selection of direct and indirect factors (indicators) that contribute to the phenomenon of water erosion.

Definition of indicators

The EO, with an agronomy profile and knowledge on soil erosion, elaborated the questionnaire and created a theoretical framework to define the meaning and application of each of the 15 indicators (Ix) in order to generate categorical responses. These indicators were grouped into six categories (Table 1).

Figure 3 Images at regional (A), local (B) and plot scale in samples taken at different dates (C-F). 

Table 1 Keys and description by category (I) and indicators (x) defined. 

Statistical design and sample size

The statistical design was based on the definition of a sample size based on the total area (23 606 ha) dedicated to dryland agriculture in the SU and an average endowment (20 ha) for this use:

()1

where

n is the sample size, t is the confidence level (at 0.95=1.96),

p is the proportion of land tenure owned by a producer relative to the total number of hectares in the producing area (20/23,606 = 0.00085), and

m is the margin of error (0.05). Although the result was n=28, in the end it was increased to 31 plots, which we visited after a completely randomly designed selection (Figure 1a) and applied the questionnaire.

Statistical analysis and hypothesis testing

We conducted the statistical analysis and hypothesis testing using the ^{Cohen’s Kappa coefficient (1960)} or Kappa concordance coefficient. In this case, the coefficient expresses the agreement between two observers, applied to two data groups, defined in six categories (I, II, III, .. c) and 15 indicators (1, 2, 3, .. ij). For its analysis, Kappa is integrated into a contingency matrix for the two data groups (a and b), represented by the responses of the two observers as A and B (Table 2).

The elements p (a=AI1 ˄ b=BI1) in Table 1 indicate the fraction that the indicator has for each category in the domain of each observer (A and B) and the diagonal line p (a=Acij ˄ b=Bcij) expresses agreement on the 15 indicators of the evaluation by both observers; and in total rows and columns p (a=Acij) and p (a=Acij) indicate the fraction corresponding to observers A and B (Table 2).

Table 2 Generic contingency matrix for the probabilistic analysis of six categories and 15 indicators. 

Obs: observer; Cat: category and p: proportion.

From the fractions of the contingency matrix (Table 2), the fraction of the observed agreement P _o and the fraction of the expected agreement (P _e ) can be calculated as follows:

()2

()3

where

i can be any of the 15 indicators used by both observers whose z-limit in the Contingency Table for a and b were defined as Acij and Bcij, respectively.

The P _o and P _e fractions were needed to calculate the degree of agreement (Yes/Yes or No/No), disagreement (Yes/No) and uncertainty (No/Don’t know) and choose the appropriate indicator, defined as:

()4

where

k is the coefficient of agreement or Kappa index (between 0 and 1). When k tends to 1 its gradient may fall into one of the following six conditions: (i) without agreement (<0), (ii) insignificant (0 - 0.2), (iii) medium (0.21-0.40), (iv) moderate (0.40 - 0.60), v) substantial (0.61 - 0.80) or vi) almost perfect (0.81 - 1.0).

The analysis of the information was performed in the descriptive statistics module of SPSS.

Evidence observed in the field

Color of soil associated with fertility

For the color of the soil associated with its fertility in its upper layer both observers showed high uncertainty, with main response “I do not know” (66 and 74 %). Questions two (I2) and three (I3) were associated with pre-sowing (fallow or subsoil) and soil organic matter content. This was in accordance with the fact that during the field study there were rains (15.8 mm and 16.4 on June 18 and 19) that caused humidity which darkened the soil in some cases (Figure 2a).

Figure 2 Type of evidence related to the management of soils and water in the plots evaluated. 

Analysis and interpretation of concordance

The concordance analysis allowed to obtain the specific measure on the degree of agreement between the OEs in each indicator; in six of them there were significant (p≤0.05) and highly significant (p≤0.001) agreements. These represented substantial agreements (Kappa=0.686), which indicated that more than half of the plots evaluated (52 %) presented evidence of adequate practices to manage rainwater, favor crops and improve the expectation of harvesting, but not to conserve the soil (Table 3).

Table 3 Results of Kapa statistical analysis to determine the degree of agreement among observers. 

Cat/Ind: category and indicators; ET: typical error; Taprox: approximate T value; SGF: statistical significance and Ik: Kappa indez.

The results also confirm the hypothesis of independence of random agreements in 40 % (6/15) of the indicators corresponding to categories I, II, IV and V (Table 3). The interpretation of these categories is as follows.

Relevance of the categories used to detect soil conservation actions

Of the six categories (Table 1), only VI (edaphic erosion) was directly related to the problem studied. In the first five categories, the pertinence and approach of their application through the indicators defined in each case, and to detect the conservation actions of the case studied would be as follows. ^{Bautista-Zúñiga et al. (2003)}, ^{Doi and Ranamukhaarachchi (2007)}, ^{Towhid (2013)} and ^{IUSS-WRB (2015)} confirmed the relevance of using soil color (Category I) and its indicators to relate it to organic matter content and its susceptibility to water erosion, mainly because Leptosols predominate in the SU. ^{Bautista-Zúñiga et al. (2003)} mentioned that in the Mayan nomenclature color is a distinctive property for Leptosols in the henequen area of Yucatan, especially for reddish-brown colors like those in Figures 3C and 3E.

Evidence tracking concerning the incorporation of crop residues (Category II) on the surface (II1) or buried (II2), as in the previous case, allows to detect current or potential erosion problems (Figure 3C-3F).

It is documented that soil cover, such as changes in soil use, can alter the hydrological cycle at different scales through changes in runoff rates, sediment yield and infiltration (^{Mzezewa and Rensburg, 2011}; ^{Heo et al., 2015}); so that in the absence of conservation practices such as the use of cover crops, no tillage, crop rotation and other protection measures or mulching, the problem of erosion can worsen without control (^{Nangia et al., 2010}; ^{Bhardwaj and Kendra, 2013}).

The effective depth of the soil in the plot (Category III) and the applied indicators (III1 and III2) are also relevant in this case, since it is a fundamental variable from which it is possible to define (at least) the productive aptitude because of its close relation with efficiency in the decomposition of the crop residues that are incorporated in the soil profile (^{Schoeneberger et al., 2012 Zou et al., 2016}).That is, both the incorporation of crop residues and soil depth are key, among others, for the evaluation of susceptibility to erosion. ^{Zou et al. (2016)} studied the return or incorporation of straw (cereals) into deep soils in a semi-arid environment (Fumeng County, China), with a precipitation similar to the SU (450 mm annually) and determined that at 15 cm depth there are the best conditions for decomposition and formation of organic C.

In all cases, the slope of the plots (Category IV) was natural, since soil management practices such as contour furrowing (IV1), terraced (IV2) or their combination (IV3) are recommended to reduce and control problems of erosion (SEMARNAT-CONAFOR, 2007; ^{Sensoy and Kara, 2014}; ^{Khaledi et al., 2016}) and to increase the availability of water in order to improve agricultural productivity (^{Nangia et al., 2010}). ^{Şensoy and Kara (2014)} studied the shape of the slope (uniform, concave and convex) and found that uniform slope, such as that prevailing in the SU (1 to 5%), for fine textured shallow soils (5 to 30 cm), had maximum sediment production levels between 3.1 and 5.5 t ha^-1; these values coincide with those by ^{López-Santos et al. (2012)} in the north of Durango, Mexico.

Water (Category V) and applied indicators (V1 and V2), just like the previous ones, were relevant because due to the water deficit for crops like maize and some forages that do not thrive with rains such as those regularly occurring in the SU (-450 mm); so to increase the availability of water the structures of conduction, diversion and land distribution are indispensable for successful crops.

^{Rashid et al. (2016)} showed that through terracing in agricultural lands located in a semi-arid climate in Pakistan (33.55° N, 72.58° E) moisture availability improved by 16 %, sediment yield decreased as well as nutrient loss, leading to a 20 % increase of wheat production.