ISSN e: 2007-4026 / ISSN print:2007-3925

### Volume 12, Issue 2 July - December 2020

ISSN: ppub: 2007-3925 epub: 2007-4026

Scientific article

# Productivity analysis of the Río Bravo irrigation districts using performance indicators

http://dx.doi.org/10.5154/r.inagbi.2018.10.022

Íñiguez-Covarrubias, Mauro 1 ; Ojeda-Bustamante, Waldo 2 * ; Olmedo-Vázquez, Víctor Manuel 3

• 1Instituto Mexicano de Tecnología del Agua. Paseo Cuauhnáhuac núm. 8532, Col. Progreso, Jiutepec, Morelos. C. P. 62550, MÉXICO.
• 2Colegio Mexicano de Ingenieros en Irrigación (COMEII). Vicente Garrido núm. 106, Col. Amp. Maravillas, Cuernavaca, Morelos, C. P. 62230, MÉXICO.
• 3Universidad Autónoma Chapingo, Centro Regional Universitario del Noroeste (CRUNO). Colima 163 Norte, Col. Centro, Ciudad Obregón, Sonora, C. P. 85000, MÉXICO.

Corresponding author: mic@tlaloc.imta.mx, tel. 777 329 3600.

Received: October 24, 2018; Accepted: May 13, 2020

## Introduction:

Irrigation districts (IDs) are irrigation projects that require periodic evaluation to determine performance.

## Objectives:

To analyze the production behavior of several IDs located in the transboundary Río Bravo basin, Mexico.

## Methodology:

Agricultural and hydrometric information was compiled, organized and analyzed for 11 IDs in the Río Bravo basin to determine production performance based on seven indicators.

The production value with respect to the volume of water extracted from the supply source varied from 1.1 to 9 $·m-3, while the productivity of water extracted from the supply source varied from 0.6 a 5.7 kg·m-3 and the production per unit of water delivered to users varied from 0.81 to 9.27 kg·m-3. ## Limitations of the study: Performance indicators reflect the productivity of the irrigation area according to management of the crop, irrigation service, technological package, crop pattern, infrastructure, among other factors. ## Originality: Performance of IDs located in the high-water pressure area in the Río Bravo basin was analyzed based on available information. ## Conclusions: Several performance indicators are required to characterize integrally IDs’ productivity, With the use of hydro-agricultural indicators it is possible to implement improvement actions, where the value of irrigation water can be maximized for the benefit of producers. Keywordsproductivity indices; conduction efficiencies; evaluation of irrigation areas ## Introduction In Mexico, irrigation districts (IDs), consisting of a delimited irrigation area, are irrigation projects established by the Federal Government through presidential decrees, since 1926, the year in which the Comisión Nacional de Irrigación was founded. IDs were created to promote national agricultural production and to ensure commercial production in times of limited or scarce rainfall. IDs have been managed, operated and maintained by the Federal Government since creation. At the beginning of 1992, the centralized federal administration, through the Comisión Nacional del Agua (CONAGUA), transferred the administration of minor distribution network and the users irrigation service through Water Users Associations (ACUs, for its acronym in Spanish), and issued the water concession rights, as well as the use of hydraulic infrastructure works. Currently, the organization of an ID is mixed, because it involves the CONAGUA, the ACUs and a Federation of ACUs known as Limited Responsibility Society (S. de R. L., for its acronym in Spanish). The ACUs are responsible for the operation, conservation, and management of the infrastructure under concession to provide the irrigation service to the users. The water delivery responsibility from the source to the farm intake are as follow: from the CONAGUA to the S. de R. L., from the S. de R. L to the ACUs and from the ACUs to the users (Palacios-Vélez, 2000). Irrigated agriculture requires various techniques for the farm irrigation application once water service is delivered to the ID users. This type of agriculture demands large capital investments and frequent maintenance of hydraulic infrastructure: dams, canals, and conduction, distribution and protection structures (CONAGUA, 1994). The analysis of performance indicators for irrigation areas requires statistical tools. Infante-Gil and Zárate-de Lara (2012) show elements of descriptive statistics and statistical inference that can be used to generate and analyze performance indicators. The productivity of an irrigated area may indirectly indicate the capacity of the irrigation infrastructure to generate the planned products and the level at which the available resources or inputs are used. The better the productivity, the higher the profitability of the ID. In this way, optimal resource management seeks to ensure that every organization manages to improve productivity with the available infrastructure and resources. The analysis of performance indicators through benchmarking applied to irrigation areas has been documented by Burt and Styles (2004) and Malano, Burton, and Makin (2004). This technique has been used to compare the water management performance of ACUs in various countries around the world (Alexander & Potter, 2004; Cakmak, Beyribey, Yildirim, & Kodal, 2004; Ruiz-Carmona, Ojeda-Bustamante, & Contijoch, 2006). Altamirano-Aguilar et al. (2017) classified and evaluated Mexico's IDs based on performance indicators, for which they grouped IDs into clusters by climate group. In this study they classified the IDs located in the Río Bravo basin, which are contemplated in the dry group in the "Water Treaty" of 1944 between Mexico and the United States of America (Mexico-USA). In the case of Bajo Río Bravo ID 025 and Bajo Río San Juan ID 026, which are located in the Bajo Bravo sub-region, Altamirano-Aguilar et al. (2017) mentioned that they belong to another climate group and, in general, the irrigation performance of all the conglomerates was reported as low. Olmedo-Vázquez, Camacho-Poyato, Rodríguez-Díaz, Minjares-Lugo, and Hernández-Hernández (2017) analyzed irrigation water use management in ACUs of ID 041, Río Yaqui, Mexico, based on eleven yield indicators and eight productivity efficiency indicators. These authors reported that most of the ACUs were inefficient (66%) in the four agricultural years analyzed, from 2010 to 2014. According to the dictionary of the Royal Spanish Academy (RAE in Spanish), productivity is a concept that describes the capacity or level of production per unit of input. In economics, productivity is understood as the link between what has been produced and the means used to achieve it (labor, materials, energy, among others), and is usually associated with efficiency and time: the less time invested in achieving the expected result, the greater the production character or performance of the system (Blanchard, 2017). Since water is a scarce resource, water use efficiency is a concept of productivity at the biological level to describe the amount of biomass accumulated (yield) as a function of the volume of water supplied (Bos, Burton, & Molden, 2005). If this term is applied to irrigated agriculture, it can be expressed in terms of yield (kg·m-3) or in economic terms regarding the unit of volume of water applied ($·m-3).

The overall conduction efficiency of an ID (m3·m-3) is given by the total volume of water delivered (m3) to users at farm intake level among the total volume of water withdrawn (m3) from supply sources (surface + groundwater). Intrinsically included in this relationship of volumes is the method of water distribution, infrastructure and regulation systems (Íñiguez-Covarrubias, de León-Mojarro, Prado-Hernández, & Rendón-Pimentel, 2007). On the other hand, the total volume of water extracted from the source of supply by irrigated area (m3·ha-1) integrates the crop water needs, farm efficiency and global conduction efficiency, being an important parameter in the water resources management of an ID.

The Secretaría de Recursos Hidráulicos (SRH, 1973), in the recommendations of the “Project Manual of Irrigation Areas”, defined the global efficiency of an ID (Edist) as the product of conduction efficiency (Econd) and farm efficiency (Eparc), for which a conduction efficiency is determined according to the type of canal lining: soil (Econd=0.7), masonry (Econd=0.75) or concrete (Econd=0.85). On the other hand, the term productivity is related to yield, since it requires good management of resources in order to achieve results that make the work carried out within the association efficient, both in the provision of the service and in the methods used and the internal relationship of the organization.

The concepts and variables associated with the main indicators for evaluating the management, planning, operation and conservation behavior of large irrigation areas are found in the study of Bos et al. (2005) By conducting an analysis of production indicators, it is possible to lay the groundwork for subsequent studies, this in order to update the indicators so that they can quantify changes in the performance of IDs in response to policies, programs, climate patterns or management of an irrigation area. In this sense, the objective of this study is to quantify and analyze the behavior of productive performance indicators of 11 IDs located in the Río Bravo basin, México.

## Materials and methods

Figure 1 shows the study region, which is the production area of the IDs located in the transboundary Río Bravo basin, Mexico, bordering the USA.

Table 1 shows the general data of the IDs studied. This information was extracted from the agricultural and hydrometric statistics compiled and published annually by CONAGUA (2017a). The supply main source is surface water; only IDs 005 and 009 report extractions from groundwater sources.

Table 1. General data of the agricultural year 2015-2016 of 11 irrigation districts in the Río Bravo basin, Mexico.

Code Name Sf Sr Vbs Vbss Vb
004 Don Martín, Coahuila-Nuevo León 18 250 4 580 97 960 0 97 960
005 Delicias, Chihuahua 73 002 61 443 839 795 4 506 844 301
006 Palestina, Coahuila 12 918 2 579 28 840 0 28 840
009 Valle de Juárez, Chihuahua 20 863 9 266 126 837 6 691 133 528
025 Bajo Río Bravo, Tamaulipas 201 291 145 064 511 139 0 511 139
026 Bajo Río San Juan, Tamaulipas 75 930 67 065 323 983 0 323 983
031 Las Lajas, Nuevo León 4 046 1 611 7 477 0 7 477
050 Acuña-Falcón, Tamaulipas 14 036 2 149 8 094 0 8 094
090 Bajo Río Conchos, Chihuahua 8 095 3 988 64 451 0 64 451
103 Río Florido, Chihuahua 8 225 4 670 69 880 0 69 880
113 Alto Río Conchos, Chihuahua 11 943 4 253 77 390 0 77 390
Sf = physical irrigable area (ha); Sr = irrigated area (ha); Vbs = gross distributed volume of surface water (hm3); Vbss = gross distributed volume of groundwater (hm3); Vb = sum of the gross distributed volumes (hm3) at the supply source level (Vb = Vbs + Vbss).

The estimation of IDs performance was obtained using the seven indicators shown in Table 2. Those performance indicators reported by Bos et al. (2005) that can be estimated with data available from official sources were chosen to evaluate IDs.

Table 2. Estimated production performance indicators for the irrigation districts (IDs) studied.

Indicators Formulation
(1) Rural average price ($·t-1) RAP = VP/Prod (2) Economic productivity of land ($·ha-1) EPL = VP/Sr
(3) Yield (t·ha-1) Yield = Prod/Sr
(4) Economic productivity of water delivered at supply source level ($·m-3) EPWf = VP/Vb (5) Water productivity at supply source (kg·m-3) WPf = Prod/Vb (6) Economic productivity of water delivered at the user level ($·m-3) EPWu = VP/Vn
(7) Water productivity at user level (kg·m-3) WPu = Prod/Vn
VP = economic value of total agricultural production of the IDs at current prices ($); Prod = total production (t); Sr = irrigated area (ha); Vb = sum of gross volumes extracted at source level (m3); Vn = net volume of water delivered to users at farm intake level (m3). The rural average price (RAP) refers to the price paid to the producer for the first-hand sale of his farm, land or production area, and does not include the economic incentive granted by the federal and state government, nor the costs of transportation and sorting when the farmer brings his product to the sales center. In other words, RAP is the current price at the time the producer makes the first sale at the plot or farm. To estimate the indicators, agricultural and hydrometric data were obtained for 15 years (2001-2002 to 2015-2016), from the agricultural statistics of the IDs reported by the CONAGUA for Vb, Sr, Vn, VP and Prod, and the financial statements of the IDs from 2012 to 2014 were used (CONAGUA, 2017b). Geospatial information on soil degradation was accessed by superimposing ID and degradation maps. This was carried out with the help of the ArcGIS v10.3 program and the data available in the Sistema Nacional de Información del Agua (SINA) of CONAGUA (2017c). For the presentation of results, "Box-Plot", also known as box-bigot diagrams were made, used to visualize the distribution of a set of data: minimum and maximum values, quartiles (Q1, Q2 or median and Q3), existence of outliers and symmetry of the distribution. To do this, it is necessary to find the median and then the two remaining quartiles. The characteristics of this type of graph are: • - The symbol * is the average of the data. • - The horizontal line across the box is the median (Q2). • - The lower side of the rectangle represents the first quartile (Q1, median of the lower half of the data or 25 % of the data), and the upper side represents the third quartile (Q3, median of the upper half of the data or 75 % of the data). Therefore, the height of the box represents the interquartile range (the difference between Q3 and Q1). • - Vertical lines (whiskers or axes) protruding from the box extend to the minimum and maximum of the data set, as long as these values do not differ from the average by more than 1.5 times the interquartile range. The ends of the whiskers are marked by two short horizontal lines. • - The values, indicated by +, below and above the whiskers, lower and upper, are considered outliers. Graphs showing the variation of the indicators in each ID studied were created. The districts were separated into two large groups, and in order to identify them in the graphs, a symbol was assigned to each ID according to Table 3. Table 3. Symbology used for the irrigation districts (IDs) of the Río Bravo basin, Mexico. Code ID Río Bravo Symbol Code ID conchos and others Symbol 04 Don Martín, Coahuila, Nuevo León 05 Delicias, Chihuahua 06 Palestina, Coahuila 31 Las Lajas, Nuevo León 09 Valle de Juárez, Chihuahua 90 Bajo Río Conchos, Chihuahua 25 Bajo Río Bravo, Tamaulipas 103 Río Florido, Chihuahua 26 Bajo Río San Juan, Tamaulipas 113 Alto Río Conchos, Chihuahua 50 Acuña-Falcón, Tamaulipas Nacional ## Results and discussion ## Performance indicators The values of the first performance indicator (RAP;$·t-1) of the 11 IDs are shown in Table 4. Due to a crop pattern concentrated in forages, the ID 006 has the lowest average RAP.

Table 4. Rural average price ($·t-1), nationwide and for 11 irrigation districts in the Río Bravo basin, Mexico. Year Irrigation district Nationwide 004 005 006 009 025 026 031 050 090 103 113 2002 1 776 353 891 1 096 992 1 151 968 1 184 2003 1 802 327 1 130 1 298 1 336 892 654 1 372 855 1 159 2004 2 533 2 891 399 1 193 1 570 880 1 173 418 1 258 1 508 1 283 2005 930 2 387 393 1 363 1 236 1 592 1 053 1 743 1 511 916 1 281 2006 1 486 1 795 979 1 402 1 539 760 1 314 2007 768 1 426 347 1 277 1 833 2 152 1 234 1 004 1 420 1 129 1 590 2008 1 814 1 929 363 1 486 2 580 2 836 1 372 1 093 1 411 1 453 1 798 2009 1 475 1 421 598 1 483 2 228 2 176 1 515 1 309 2 083 1 337 1 882 2010 1 698 1 717 561 1 857 2 129 2 269 1 394 1 604 1 949 2 604 1 985 2011 1 998 1 687 676 2 548 3 196 3 537 2 507 1 757 2 351 2 104 2 290 2012 1 955 1 475 565 1 290 3 397 4 321 2 189 1 869 566 940 2 394 2013 1 994 1 888 624 1 235 3 436 3 561 3 011 1 836 697 616 2 277 2014 1 781 1 464 670 1 632 2 923 3 604 2 601 2 047 806 706 4 065 2 315 2015 2 547 2 276 677 1 481 3 388 3 301 2 352 921 958 9 355 2 566 2016 2 519 1 960 647 1 578 3 129 3 332 2 660 2 533 1 147 1 014 12 017 2 818 Figure 2 shows the RAP per crop year for each ID, and the national average value is reported as a reference. A problem when valuing agricultural production at current prices is the effects on the fluctuations in the RAP of production volumes, so it is recommended to carry out an analysis at constant prices to remove these effects and homogenize the values of each year with respect to the base year (Kennedy, 2016). Table 5 shows the results of the descriptive statistics and the results associated with the RAP of the IDs studied. The statistics obtained are the basis of Figure 3. This graph shows high variability in the average of the RAP, and a greater variability in the IDs 025, 026 and 031, due to their crop pattern. Table 5. Descriptive statistics of the rural average price ($·t-1) of 11 irrigation districts in the Río Bravo basin, Mexico.

Statistics Irrigation district
004 005 006 009 025 026 031 050 090 103 113
Average 1 834 1 864 514 1 460 2 416 2 519 1 684 1 544 1 345 1 191 8 479
Median 1 885 1 789 563 1 422 2 404 2 269 1 383 1 674 1 372 968 9 355
Standard Deviation 575 418 141 393 833 1 060 742 607 506 545 4 048
Minimum 768 1 421 327 891 1 236 880 892 418 566 616 4 065
Maximum 2 547 2 892 677 2 548 3 436 4 321 3 011 2 533 2 351 2 604 12 017
Quartile 25 % 1 531 1 472 360 1224 1 549 1 592 1 038 1 071 921 855 4 065
Quartile 75 % 2 389 2 039 652 1 592 3 244 3 537 2 531 1 914 1 539 1 453 12 017
Lower whisker 768 1 421 327 891 1,236 880 892 418 566 616 4 065
Upper whisker 2 547 2 892 677 2 548 3 436 4 321 3 011 2 533 2 351 2 604 12 017

The second production indicator studied was the economic productivity of land (EPL; thousands of $·ha-1). Table 6 shows the EPL results for the 11 IDs analyzed and the nationwide value. Gaps can be observed because data from some IDs were not available. Table 6. Economic land productivity value (thousands of$·ha-1) of 11 irrigation districts in the Río Bravo basin and nationwide, Mexico.

Year Irrigation district Nationwide
004 005 006 009 025 026 031 050 090 103 113
2002 21.85 8.14 14.47 4.52 6.04 13.17 13.71 18.05
2003 23.27 8.15 15.10 5.63 5.33 7.61 4.97 17.08 10.86 17.83
2004 36.18 35.62 9.12 15.65 9.55 8.24 4.18 7.63 15.32 15.19 22.19
2005 3.58 30.00 9.50 17.56 5.75 9.29 5.43 29.35 19.05 16.25 19.86
2006 6.97 9.70 5.03 15.60 21.01 15.43 20.80
2007 6.40 30.89 6.77 16.96 8.68 12.52 3.92 14.55 18.51 17.57 25.51
2008 8.73 38.53 5.95 19.42 11.68 14.23 8.83 27.48 13.45 24.76 28.89
2009 13.80 30.12 10.72 22.21 10.11 11.81 5.95 32.78 21.50 19.12 28.60
2010 17.89 35.72 10.64 28.96 11.23 11.32 6.78 51.24 24.53 21.76 30.71
2011 18.91 34.24 15.36 25.50 13.84 15.09 9.75 40.76 29.36 45.90 34.52
2012 17.86 39.76 12.14 25.57 17.97 25.76 11.95 52.21 27.12 40.79 42.36
2013 20.37 46.80 11.60 24.83 16.17 20.38 14.57 47.86 32.44 25.31 39.49
2014 16.26 40.50 13.38 32.32 15.50 23.24 11.12 51.45 34.26 22.33 61.68 37.97
2015 28.67 66.26 13.85 37.62 20.04 22.79 77.50 45.48 32.24 93.51 45.28
2016 34.66 81.13 13.95 38.27 18.61 22.74 10.35 83.96 54.91 34.61 110.53 51.48

Figure 4 shows the EPL per agricultural year of the ID in the Río Bravo basin and the nationwide value reported in Table 7.

Table 7. Descriptive statistics of land economic productivity (thousands of $·ha-1) of 11 irrigation districts in the Río Bravo basin, Mexico. Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 18.61 39.62 10.66 23.89 12.27 14.47 7.97 38.38 25.81 23.72 88.57 Median 17.87 35.67 10.68 23.52 11.46 12.52 7.19 36.77 21.50 21.76 93.51 Standard deviation 10.33 16.15 2.87 8.05 4.82 6.91 3.21 24.20 11.97 10.37 24.80 Minimum 3.58 21.85 5.95 14.47 5.63 4.52 3.92 4.97 13.17 10.86 61.68 Maximum 36.18 81.13 15.36 38.27 20.04 25.76 14.57 83.96 54.91 45.90 110.53 Quartile 25 % 9.99 30.09 8.15 16.63 8.25 9.29 5.33 15.34 17.08 15.43 61.68 Quartile 75 % 26.59 42.08 13.50 29.80 16.62 22.74 10.54 51.64 32.44 32.24 110.53 Lower whisker 3.58 21.85 5.95 14.47 5.63 4.52 3.92 4.97 13.17 10.86 61.68 Upper whisker 36.18 72.42 15.36 38.27 20.04 25.76 14.57 83.96 54.91 45.90 110.53 Table 7 shows the results of the descriptive statistics of the EPL of ID in the Río Bravo basin. These statistics are the basis of Figure 5, where the ID 050 had the greatest dispersion. The third production indicator analyzed was yield (t·ha-1). Table 8 shows the values of this indicator for the 11 IDs and the nationwide value. It is worth mentioning that the agricultural year from 2005-2006 was very dry for several studied; therefore, IDs 004, 005, 006 and 009 did not establish irrigated area (Table 6). Table 8. Yield (t·ha-1) obtained for 11 irrigation districts in the Río Bravo basin and the nationwide value, Mexico. Year Irrigation district Nationwide 004 005 006 009 025 026 031 050 090 103 113 2002 12.30 23.05 16.24 4.13 6.09 11.44 14.17 15.24 2003 12.91 24.95 13.36 4.34 3.99 8.53 7.60 12.45 12.70 15.38 2004 14.29 12.32 22.84 13.12 6.09 9.36 3.57 18.28 12.18 10.08 17.30 2005 3.85 12.57 24.18 12.89 4.65 5.84 5.16 16.83 12.61 17.75 15.50 2006 4.69 5.40 5.14 11.12 13.65 20.31 15.83 2007 8.33 21.66 19.52 13.27 4.74 5.82 3.18 14.49 13.04 15.56 16.04 2008 4.81 19.98 16.40 13.06 4.53 5.02 6.44 25.15 9.53 17.04 16.06 2009 9.36 21.20 17.93 14.98 4.54 5.43 3.93 25.04 10.32 14.31 15.20 2010 10.53 20.80 18.98 15.60 5.28 4.99 4.86 31.95 12.58 8.36 15.47 2011 9.47 20.29 22.71 10.01 4.33 4.27 3.89 23.20 12.49 21.81 15.07 2012 9.13 26.97 21.48 19.83 5.29 5.96 5.46 27.93 47.92 43.41 17.70 2013 10.21 24.79 18.60 20.11 4.70 5.72 4.84 26.07 46.53 41.10 17.34 2014 9.13 27.66 19.96 19.81 5.30 6.45 4.28 25.14 42.51 31.65 15.17 16.40 2015 11.25 29.12 20.44 25.39 5.91 6.90 32.95 49.40 33.64 10.00 17.65 2016 13.76 41.39 21.58 24.25 5.95 6.83 3.89 33.15 47.88 34.13 9.20 18.27 Figure 6 represents the yield per agricultural year of the ID in the Río Bravo basin and the nationwide value reported in Table 8. Table 9 shows the results of the descriptive statistical measurements of the yield of the ID in the Río Bravo basin. These measurements are the basis of Figure 7. Table 9. Descriptive yield measurements (t·ha-1) of 11 irrigation districts in the Río Bravo basin, Mexico. Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 9.51 21.71 20.90 16.57 5.02 5.74 4.95 22.78 23.64 22.40 11.46 Median 9.41 21.00 20.96 15.29 4.72 5.72 4.85 25.09 12.61 17.75 10.00 Standard deviation 3.03 8.13 2.49 4.61 0.61 1.35 1.40 8.04 17.08 11.40 3.24 Minimum 3.84 12.30 16.40 10.01 4.33 3.99 3.18 7.60 9.53 8.36 9.20 Maximum 14.29 41.39 24.95 25.39 6.09 9.36 8.53 33.15 49.40 43.41 15.17 Quartile 25 % 8.53 12.83 18.88 13.10 4.54 4.99 3.89 16.25 12.18 14.17 9.20 Quartile 75 % 11.07 27.14 22.89 19.90 5.46 6.45 5.62 28.93 46.53 33.64 15.17 Lower whisker 4.72 12.30 16.40 10.01 4.33 3.99 3.18 7.60 9.53 8.36 9.20 Upper whisker 14.29 41.39 24.95 25.39 6.09 9.36 8.53 33.15 49.40 43.41 15.17 The values obtained from the yield were very variable in IDs 005, 050, 090 and 103, this due to the mixture of forage crops and grains. This indicates that the interdistrict comparison of yield, as a single value for each agricultural year (Tables 8 and 9), is complicated by the fact that there is inter- and interdistrict variation in crop patterns and seasons, because it generates an overestimation of the production of perennial forage and horticultural crops over grains. This is due to the fact that different production organs, which have different humidity, are compared in relation to the yield, that is, green matter against dry matter. The fourth production indicator studied is the economic productivity of water at source (EPWf;$·m-3). Table 10 shows the results of this indicator for the 11 IDs and nationwide.

Table 10. Economic productivity of water at level of the supply source ($·m-3) of 11 irrigation districts in the Río Bravo basin and nationwide, Mexico. Year Irrigation district Nationwide 004 005 006 009 025 026 031 050 090 103 113 2002 1.09 0.82 0.85 0.77 0.60 0.70 0.76 1.3 2003 1.41 1.15 0.90 2.15 0.91 1.21 1.98 0.84 0.62 1.6 2004 12.01 2.07 2.19 1.11 2.31 1.77 0.36 3.21 1.13 0.91 1.8 2005 0.19 1.54 0.90 1.32 1.50 1.29 0.43 4.58 1.00 0.86 1.6 2006 1.59 1.31 0.59 3.05 1.25 1.00 1.6 2007 0.55 1.88 0.65 1.28 2.30 2.28 0.60 5.54 1.33 0.97 2.0 2008 0.55 2.71 0.50 1.49 2.12 1.85 0.76 8.65 0.83 1.85 2.2 2009 0.72 1.55 0.71 1.41 2.06 1.75 0.53 6.48 1.20 1.07 2.2 2010 1.26 2.15 1.44 1.78 3.23 2.60 0.92 8.21 1.37 1.62 2.5 2011 1.03 1.81 1.04 1.89 2.10 1.95 0.71 9.19 1.42 2.51 2.0 2012 1.27 2.34 1.09 1.85 3.28 3.57 1.08 12.69 2.03 2.59 3.9 2013 1.27 3.23 1.07 1.74 4.68 3.32 1.64 12.60 2.38 1.68 3.7 2014 1.00 2.72 0.94 2.49 5.72 4.81 2.00 8.98 2.33 1.47 2.82 3.5 2015 1.79 4.58 1.63 2.36 7.49 7.52 20.09 2.72 1.84 4.47 3.7 2016 1.62 5.89 1.25 2.53 5.28 4.71 2.23 22.29 3.40 2.31 6.07 4.0 Figure 8 shows the EPWf per agricultural year of the ID in the Río Bravo basin and nationwide reported in Table 10. Table 11 shows the results of the descriptive statistics of EPWf of ID of the Rio Bravo Basin. These statistics are the basis of Figure 9, where ID 050 has the greatest variability. Table 11. Descriptive statistics of the economic productivity of water at level of the supply source ($·m-3) of 11 irrigation districts in the Río Bravo basin, Mexico.

Statistics Irrigation district
004 005 006 009 025 026 031 050 090 103 113
Average 1.94 2.50 1.10 1.64 3.27 2.70 0.98 9.11 1.59 1.47 4.45
Median 1.15 2.11 1.05 1.61 2.31 1.95 0.74 8.43 1.33 1.47 4.47
Standard deviation 3.20 1.32 0.44 0.55 1.82 1.83 0.59 6.09 0.79 0.65 1.63
Minimum 0.19 1.09 0.50 0.85 1.50 0.77 0.36 1.98 0.70 0.62 2.82
Maximum 12.01 5.89 2.19 2.53 7.49 7.52 2.23 22.29 3.40 2.59 6.07
Quartile 25 % 0.59 1.55 0.79 1.24 2.09 1.31 0.57 4.24 1.00 0.91 2.82
Quartile 75 % 1.53 2.85 1.30 2.01 4.83 3.57 1.32 12.63 2.33 1.85 6.07
Lower whisker 0.19 1.09 0.50 0.85 1.50 0.77 0.36 1.98 0.70 0.62 2.82
Upper whisker 3.55 5.48 2.19 2.53 7.49 7.52 2.23 22.29 3.40 2.59 6.07

The fifth production indicator studied was water productivity at the source of supply level (WPf; kg·m-3). Table 12 shows the results obtained for this indicator for the 11 IDs and nationwide.

Table 12. Water productivity at the level of the supply source (kg·m-3) of 11 irrigation districts in the Río Bravo basin and nationwide, Mexico.

Year Irrigation district Nationwide
004 005 006 009 025 026 031 050 090 103 113
2002 0.62 2.33 0.95 0.70 0.60 0.61 0.78 0.99
2003 0.78 3.51 0.80 1.65 0.68 1.36 3.04 0.61 0.73 1.23
2004 4.74 0.72 5.48 0.93 1.47 2.01 0.30 7.69 0.90 0.60 1.18
2005 0.21 0.65 2.28 0.97 1.21 0.81 0.41 2.63 0.66 0.94 1.09
2006 1.07 0.73 0.60 2.17 0.81 1.32 1.07
2007 0.72 1.32 1.89 1.00 1.26 1.06 0.48 5.52 0.94 0.86 1.14
2008 0.30 1.40 1.38 1.00 0.82 0.65 0.56 7.92 0.59 1.27 1.09
2009 0.49 1.09 1.19 0.95 0.92 0.80 0.35 4.95 0.58 0.80 1.01
2010 0.74 1.25 2.57 0.96 1.52 1.15 0.66 5.12 0.71 0.62 1.13
2011 0.52 1.07 1.54 0.74 0.66 0.55 0.28 5.23 0.60 1.19 0.76
2012 0.65 1.59 1.93 1.43 0.96 0.83 0.49 6.79 3.59 2.75 1.48
2013 0.63 1.71 1.71 1.41 1.36 0.93 0.54 6.87 3.41 2.72 1.43
2014 0.56 1.86 1.40 1.53 1.96 1.34 0.77 4.39 2.89 2.08 0.69 1.28
2015 0.70 2.02 2.41 1.59 2.21 2.28 8.54 2.95 1.91 0.48 1.26
2016 0.64 3.00 1.93 1.60 1.69 1.41 0.84 8.80 2.96 2.28 0.51 1.27

Figure 10 shows the WPf per agricultural year of the ID in the Río Bravo basin and nationwide reported in Table 12. Most of the values obtained are below the baseline of 1.62 kg·m-3 established for 2012 in the “National Development Plan 2013-2018” (CONAGUA, 2014), and the target for 2018 that was established at 1.87 kg·m-3; only five IDs had higher values in 2016.

Table 13 shows the results of the descriptive statistics of the WPf of the ID of the Rio Bravo basin. These values are the basis of Figure 11, where DR 050 is the one with the greatest variability in values.

Table 13. Descriptive statistics of water productivity at level of supply source (kg·m-3) of 11 irrigation districts in the Rio Bravo basin, Mexico.

Statistics Irrigation district
004 005 006 009 025 026 031 050 090 103 113
Average 0.91 1.36 2.25 1.13 1.34 1.06 0.59 5.69 1.52 1.39 0.56
Median 0.64 1.28 1.93 0.98 1.31 0.83 0.55 5.37 0.81 1.19 0.51
Standard deviation 1.22 0.65 1.11 0.31 0.44 0.51 0.27 2.17 1.22 0.76 0.12
Minimum 0.20 0.62 1.19 0.74 0.66 0.55 0.28 2.17 0.58 0.60 0.48
Maximum 4.74 3.00 5.48 1.60 2.21 2.28 1.36 8.80 3.59 2.75 0.69
Quartile 25 % 0.49 0.76 1.50 0.95 0.95 0.70 0.40 4.05 0.61 0.78 0.48
Quartile 75 % 0.71 1.75 2.45 1.46 1.66 1.34 0.69 7.75 2.95 2.08 0.69
Lower whisker 0.20 0.62 1.19 0.74 0.66 0.55 0.28 2.17 0.58 0.60 0.48
Upper whisker 1.47 3.00 4.35 1.60 2.21 2.28 1.30 8.80 3.59 2.75 0.69

The sixth production indicator evaluated was the economic productivity of water at the user level (EPWu; $·m-3). Table 14 shows the results of that indicator for 11 IDs of the agricultural years with data availability. Table 14. Water economic productivity at user level ($·m-3) of 11 irrigation districts of the Rio Bravo basin, Mexico.

Year Irrigation district
004 005 006 009 025 026 031 050 090 103 113
2012 2.64 3.73 2.76 3.14 6.77 5.94 1.51 16.40 3.62 4.02
2013 3.06 6.87 2.92 3.41 8.41 5.21 2.18 16.28 4.32 2.66
2014 2.43 4.70 3.00 4.23 10.32 7.33 2.32 11.60 4.48 2.10 4.42
2015 3.79 6.92 5.70 3.89 16.59 11.85 27.47 5.34 3.21 7.56
2016 3.50 8.65 3.42 4.10 10.38 6.95 2.48 28.80 6.67 3.56 9.28

Table 15 shows the results of the descriptive statistics of the EPWu for the ID in the Río Bravo basin. These values are the basis of Figure 12, where the high variability in water availability of ID 050 can be seen, which may be due to the cultivation pattern based on forage and fruit trees. Olmedo et al. (2017) report average EPWu values in the range of 2.8 to 6 $·m-3 for the ID 041, which are very similar to those estimated in this study, where the main crop is wheat grain. Table 15. Descriptive statistics of economic water productivity at the user level ($·m-3) of 11 irrigation districts in the Río Bravo basin, Mexico.

Statistics Irrigation district
04 05 06 09 025 026 031 050 090 103 113
Average 3.09 6.18 3.56 3.75 10.50 7.46 2.12 20.11 4.88 3.11 7.08
Median 3.06 6.87 3.00 3.89 10.32 6.95 2.25 16.40 4.48 3.21 7.56
Standard deviation 0.57 1.96 1.22 0.46 3.72 2.59 0.43 7.59 1.17 0.76 2.47
Minimum 2.43 3.73 2.76 3.14 6.77 5.21 1.51 11.60 3.62 2.10 4.42
Maximum 3.79 8.65 5.70 4.23 16.59 11.85 2.48 28.80 6.67 4.02 9.28
Quartile 25 % 2.54 4.22 2.84 3.28 7.59 5.58 1.67 13.94 3.97 2.38 4.42
Quartile 75 % 3.65 7.79 4.56 4.17 13.49 9.59 2.44 28.14 6.00 3.79 9.28
Lower whisker 2.43 3.73 2.76 3.14 6.77 5.21 1.51 11.60 3.62 2.10 4.42
Upper whisker 3.79 8.65 5.70 4.23 16.59 11.85 2.48 28.80 6.67 4.02 9.28

The last production indicator studied was water productivity at user level (WPu; kg·m-3). Table 16 shows the results of this indicator for the 11 IDs of the agricultural years with data availability.

Table 16. Water productivity at user level (kg·m-3) of 11 irrigation districts of the Rio Bravo basin, Mexico.

Year Irrigation district
004 005 006 009 025 026 031 050 090 103 113
2012 1.35 2.53 4.88 2.44 1.99 1.38 0.69 8.77 6.39 4.28
2013 1.54 3.64 4.68 2.76 2.45 1.46 0.72 8.87 6.20 4.32
2014 1.37 3.21 4.47 2.59 3.53 2.03 0.89 5.67 5.55 2.97 1.09
2015 1.49 3.04 8.42 2.62 4.90 3.59 11.68 5.80 3.35 0.81
2016 1.39 4.41 5.28 2.60 3.32 2.09 0.93 11.37 5.82 3.51 0.77

Table 17 shows the results of the descriptive statistics of the WPu of 11 ID in the Río Bravo Basin. These statistics are the basis of Figure 13, where IDs 005, 006, 025, 026, 050 and 103 show between medium and high variability; this is due to the uncertainty in the volumes delivered at the user level due to the lack of reliable estimates, as reported by Alexander (2002) for ID 041 in Mexico. Another factor may be the year-to-year change in cropping plans due to the variability in annual availability at the source level, as is the case of IDs 025 and 026.

Table 17. Descriptive statistics for water productivity at the user level (kg·m-3) of 11 irrigation districts in the Río Bravo basin, Mexico

Statistics Irrigation district
004 005 006 009 025 026 031 050 090 103 113
Average 1.43 3.37 5.55 2.60 3.24 2.11 0.81 9.27 5.95 3.69 0.89
Median 1.39 3.21 4.88 2.60 3.32 2.03 0.81 8.87 5.82 3.51 0.81
Standard deviation 0.08 0.71 1.63 0.11 1.12 0.89 0.12 2.43 0.34 0.59 0.17
Minimum 1.35 2.53 4.47 2.44 1.99 1.38 0.69 5.67 5.55 2.97 0.77
Maximum 1.54 4.41 8.42 2.76 4.90 3.59 0.93 11.68 6.39 4.32 1.09
Quartile 25 % 1.36 2.79 4.58 2.52 2.22 1.42 0.70 7.22 5.67 3.16 0.77
Quartile 75 % 1.51 4.03 6.85 2.69 4.21 2.84 0.92 11.52 6.30 4.30 1.09
Lower whisker 1.35 2.53 4.47 2.44 1.99 1.38 0.69 5.67 5.55 2.97 0.77
Upper whisker 1.54 4.41 8.42 2.76 4.90 3.59 0.93 11.68 6.39 4.32 1.09

If EPL (thousands $·ha-1) and yield (t·ha-1) are related, then RAP (Equation 1) is obtained. R A P = E P L Y i e l d = V P S r P r o d S r = V P P r o d = ($ ) ( t )

With regard to total production (Prod), if we consider RAP, yield, WPf and WPu, we can see that as production increases, the values of the indicators increase. Table 18 shows the average values of each production performance indicator per ID.

Table 18. Average values of the seven indicators evaluated per irrigation district in the Río Bravo basin and nationwide, Mexico.

Indicator Irrigation district Nationwide
004 005 006 009 025 026 031 050 090 103 113
(1) RAP ($·t-1) 1834 1864 514 1460 2416 2519 1684 1544 1345 1191 8479 1875.7 (2) EPL (thousand$·ha-1) 18.61 39.62 10.66 23.9 12.27 14.47 7.97 38.4 25.8 23.72 88.6 30.9
(3) Yield (t·ha-1) 9.51 21.71 20.9 16.6 5.02 5.74 4.95 22.8 23.6 22.4 11.5 16.3
(4) EPWf ($·m-3) 1.94 2.5 1.1 1.64 3.27 2.7 0.98 9.11 1.59 1.47 4.45 1.17 (5) WPf (kg·m-3) 0.91 1.36 2.25 1.13 1.34 1.06 0.59 5.69 1.52 1.39 0.56 0.99 (6) EPWu ($·m-3) 3.09 6.18 3.56 3.75 10.5 7.46 2.12 20.1 4.88 3.11 7.08 -
(7) WPu (kg·m-3) 1.43 3.37 5.55 2.6 3.24 2.11 0.81 9.27 5.95 3.69 0.89 -

The estimated values of the seven performance indicators are within the range reported by Altamirano-Aguilar et al. Table 19 shows an analysis of the indicators with respect to their average, highlighting the districts with the highest and lowest values. IDs 031, 050 and 113 show the values with the highest dispersion with respect to the average of the basin ID. The data reported in this table indicate that it is not feasible to use a single indicator to evaluate performance, but several complementary indicators are required to characterize ID integrally, this is due to the complexity of the agronomic, environmental, political and socio-economic factors defining water and land productivity of ID.

Table 19. Average values of the distribution of seven performance indicators of 11 irrigation districts (ID) in the Río Bravo basin, Mexico (from 2002 to 2016)

Indicator Average Reference range
Intermediate Low High
(1) RAP ($·t-1) 2 259.09 514 (ID 006) 8 479 (ID 113) 325 - 16 572 (2) EPL (thousand$·ha-1) 27.63 7.97 (ID 031) 88.57 (ID 113) 8.8 - 226.0
(3) Yield (t·ha-1) 14.97 4.95 (ID 031) 23.64 (ID 090) 4.4 - 102.6
(4) EPWf ($·m-3) 2.80 1.1 (ID 006) 9.11 (ID 050) 0.38 - 20.3 (5) WPf (kg·m-3) 1.62 0.56 (ID 113) 5.7 (ID 050) 0.50 - 26.2 (6) EPWu ($·m-3) 6.53 2.12 (ID 031) 20 (ID 050) 1.0 - 21.47
(7) WPu (kg·m-3) 3.54 0.89 (ID 113) 9.27 (ID 050) 0.75 - 37.1
The data in brackets indicates the irrigation district with the highest or lowest average value. The reference column is based on the study of Altamirano-Aguilar et al. (2017).

Indicators regarding the value of production (VP) at current prices, as is the case of RAP, show a positive trend (Figure 14) due to the effect of the increase in production costs and inflation.

Since there is great variation between indicator values at the ID level, a more detailed analysis at the irrigation module level is recommended. This is because each irrigation module is autonomous, and they are responsible for delivering the irrigation service to the users and conserving the hydro-agricultural infrastructure under concession.

Table 20 shows a dispersion analysis of the production per unit of water extracted from the supply source of the 11 IDs.

Table 20. Analysis of water productivity dispersion at level of the supply source (WPf) per irrigation district (IDs) analyzed.

ID WPf Highlights
004 It has outliers of 0.21 and 4.74 kg·m-3. In 2016, it had a productivity of 0.64 kg·m-3, which is equal to the Median.
005 It has upward values and Upper Whisker limits of 3 kg·m-3.
006 Part of high values. In 2016, it had a productivity of 1.93 kg·m-3, which was lower than in 2015.
009 It shows an increase since 2009, with the highest value in 2016 of 1.60 kg·m-3.
025 It shows ups and downs greater than the Median (1.31 kg·m-3), with a Maximum of 2.21 kg·m-3 in 2015. In the period evaluated it showed an average of 1.34 kg·m-3.
026 Values oscillate mainly in the range of 0.65 to 1.4 kg·m-3, with an outlier Maximum value of 2.28 and an average value of 1.06 kg·m-3.
031 It shows little variation in values, with a small positive trend in the analysis period and a high outlier of 1.36 kg·m-3 in 2003.
050 It starts with high values, and during the period evaluated shows values higher than 7.75 kg·m-3 and a Median of 5.37 kg·m-3. In 2016 it had the highest productivity of all the IDs, with a value of 8.80 kg·m-3.
090 It started with low values, and from 2012 productivity increased above the average and Median, with an outlier of 3.59 kg·m-3.
103 It starts with low values, and from 2012 productivity increased above the average and Median, with an outlier of 2.75 kg·m-3.
113 It has very few available data. In 2016 it had values equal to the Median (0.51 kg·m-3).

By studying the correlation of two production performance indicators, it is possible to determine the conduction efficiency (CE) of the supply source to the farm intake, where it is delivered to the user. In this case, the related indicators are WPf and WPu, as shown in the following equation:

C E = W P f W P u = ( P r o d / V b ) ( P r o d / V n ) = V b V n = m 3 m 3

Table 21 shows the conduction efficiencies obtained from Equation 2 of the 11 IDs studied, and Figure 15 shows the efficiencies of IDs 004 and 005, where ID 050 stands out. It is worth mentioning that most Mexican IDs were designed with a conduction efficiency of 70%, assuming earth-lined channels (SRH, 1973).

Table 21. Conduction efficiencies of 11 irrigation districts in the Rio Bravo basin, Mexico

Year Irrigation districts
004 005 006 009 025 026 031 050 090 103 113
2012 0.48 0.63 0.39 0.59 0.48 0.6 0.72 0.77 0.56 0.64
2013 0.41 0.47 0.37 0.51 0.56 0.64 0.75 0.77 0.55 0.63
2014 0.41 0.58 0.31 0.59 0.55 0.66 0.86 0.77 0.52 0.7 0.64
2015 0.47 0.66 0.29 0.61 0.45 0.63 0.73 0.51 0.57 0.59
2016 0.46 0.68 0.37 0.62 0.51 0.68 0.9 0.77 0.51 0.65 0.65

In general, conduction efficiencies remained almost constant over the five years studied. Based on the results obtained (Table 21 and Figure 15), it can be deduced that the large investments made to improve the conduction network of many IDs have not translated into a significant increase in conduction efficiency, from the source of supply to the farm. This was possibly coupled with limited conservation of the IDs studied.

## Conclusions

The most common indicators for evaluating the performance of an ID in Mexico are yield and global conduction efficiency. However, as the results indicate, no single performance indicator can be used, but several complementary indicators are required to characterize IDs, integrally. Inter-district comparison of indicator values is complicated due to district variation in cropping cycles and patterns, resulting in an overestimation of the production of perennial forage and horticultural crops over grains.

The values of conduction efficiency of hydraulic infrastructure of IDs are below those contemplated in the original design of IDs. This indicates a degradation of the irrigation infrastructure, possibly due to limited conservation or operation of the IDs studied.

The productive performance of IDs is low due to a series of structural and non-structural factors that limit development at the irrigation area level. Some of the factors are low efficiency of conduction network (from the supply source to the farm), high inter-annual variability of available volumes at the source level, low irrigation fee, low technological level and increase in production costs, among others.

It is recommended to carry out the performance analysis per irrigation module and, to be not only productive, but also operational and administrative. This is the responsibility of the ACUs, because they are responsible for delivering the irrigation service to the users and for conserving the hydro-agricultural infrastructure under concession.

To dispose of unused water, one way is to improve planning, distribution and conservation of the distribution network. In addition, it is necessary to conduct a more detailed analysis of the irrigation service offered by the ACUs based on performance indicators at the ACU level, and not integrally as shown in this study.

The indicators used and results obtained can be used to evaluate the production behavior of IDs, as well as to analyze the investment policies to improve the hydro-agricultural infrastructure (both of the distribution network and of the farm technification), and agricultural policies of subsidies through guarantee prices and support to the agricultural areas under irrigation. This should be reflected in a change in performance indicators, since the value of irrigation water should be maximized for the benefit of producers and society.

## References

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### Tables:

Table 1. General data of the agricultural year 2015-2016 of 11 irrigation districts in the Río Bravo basin, Mexico.
Code Name Sf Sr Vbs Vbss Vb
004 Don Martín, Coahuila-Nuevo León 18 250 4 580 97 960 0 97 960
005 Delicias, Chihuahua 73 002 61 443 839 795 4 506 844 301
006 Palestina, Coahuila 12 918 2 579 28 840 0 28 840
009 Valle de Juárez, Chihuahua 20 863 9 266 126 837 6 691 133 528
025 Bajo Río Bravo, Tamaulipas 201 291 145 064 511 139 0 511 139
026 Bajo Río San Juan, Tamaulipas 75 930 67 065 323 983 0 323 983
031 Las Lajas, Nuevo León 4 046 1 611 7 477 0 7 477
050 Acuña-Falcón, Tamaulipas 14 036 2 149 8 094 0 8 094
090 Bajo Río Conchos, Chihuahua 8 095 3 988 64 451 0 64 451
103 Río Florido, Chihuahua 8 225 4 670 69 880 0 69 880
113 Alto Río Conchos, Chihuahua 11 943 4 253 77 390 0 77 390
Sf = physical irrigable area (ha); Sr = irrigated area (ha); Vbs = gross distributed volume of surface water (hm3); Vbss = gross distributed volume of groundwater (hm3); Vb = sum of the gross distributed volumes (hm3) at the supply source level (Vb = Vbs + Vbss).
Table 2. Estimated production performance indicators for the irrigation districts (IDs) studied.
Indicators Formulation
(1) Rural average price ($·t-1) RAP = VP/Prod (2) Economic productivity of land ($·ha-1) EPL = VP/Sr
(3) Yield (t·ha-1) Yield = Prod/Sr
(4) Economic productivity of water delivered at supply source level ($·m-3) EPWf = VP/Vb (5) Water productivity at supply source (kg·m-3) WPf = Prod/Vb (6) Economic productivity of water delivered at the user level ($·m-3) EPWu = VP/Vn
(7) Water productivity at user level (kg·m-3) WPu = Prod/Vn
VP = economic value of total agricultural production of the IDs at current prices ($); Prod = total production (t); Sr = irrigated area (ha); Vb = sum of gross volumes extracted at source level (m3); Vn = net volume of water delivered to users at farm intake level (m3). Table 3. Symbology used for the irrigation districts (IDs) of the Río Bravo basin, Mexico. Code ID Río Bravo Symbol Code ID conchos and others Symbol 04 Don Martín, Coahuila, Nuevo León 05 Delicias, Chihuahua 06 Palestina, Coahuila 31 Las Lajas, Nuevo León 09 Valle de Juárez, Chihuahua 90 Bajo Río Conchos, Chihuahua 25 Bajo Río Bravo, Tamaulipas 103 Río Florido, Chihuahua 26 Bajo Río San Juan, Tamaulipas 113 Alto Río Conchos, Chihuahua 50 Acuña-Falcón, Tamaulipas Nacional Table 4. Rural average price ($·t-1), nationwide and for 11 irrigation districts in the Río Bravo basin, Mexico.
Year Irrigation district Nationwide
004 005 006 009 025 026 031 050 090 103 113
2002 1 776 353 891 1 096 992 1 151 968 1 184
2003 1 802 327 1 130 1 298 1 336 892 654 1 372 855 1 159
2004 2 533 2 891 399 1 193 1 570 880 1 173 418 1 258 1 508 1 283
2005 930 2 387 393 1 363 1 236 1 592 1 053 1 743 1 511 916 1 281
2006 1 486 1 795 979 1 402 1 539 760 1 314
2007 768 1 426 347 1 277 1 833 2 152 1 234 1 004 1 420 1 129 1 590
2008 1 814 1 929 363 1 486 2 580 2 836 1 372 1 093 1 411 1 453 1 798
2009 1 475 1 421 598 1 483 2 228 2 176 1 515 1 309 2 083 1 337 1 882
2010 1 698 1 717 561 1 857 2 129 2 269 1 394 1 604 1 949 2 604 1 985
2011 1 998 1 687 676 2 548 3 196 3 537 2 507 1 757 2 351 2 104 2 290
2012 1 955 1 475 565 1 290 3 397 4 321 2 189 1 869 566 940 2 394
2013 1 994 1 888 624 1 235 3 436 3 561 3 011 1 836 697 616 2 277
2014 1 781 1 464 670 1 632 2 923 3 604 2 601 2 047 806 706 4 065 2 315
2015 2 547 2 276 677 1 481 3 388 3 301 2 352 921 958 9 355 2 566
2016 2 519 1 960 647 1 578 3 129 3 332 2 660 2 533 1 147 1 014 12 017 2 818
Figure 2 shows the RAP per crop year for each ID, and the national average value is reported as a reference. A problem when valuing agricultural production at current prices is the effects on the fluctuations in the RAP of production volumes, so it is recommended to carry out an analysis at constant prices to remove these effects and homogenize the values of each year with respect to the base year (Kennedy, 2016).
Table 5. Descriptive statistics of the rural average price ($·t-1) of 11 irrigation districts in the Río Bravo basin, Mexico. Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 1 834 1 864 514 1 460 2 416 2 519 1 684 1 544 1 345 1 191 8 479 Median 1 885 1 789 563 1 422 2 404 2 269 1 383 1 674 1 372 968 9 355 Standard Deviation 575 418 141 393 833 1 060 742 607 506 545 4 048 Minimum 768 1 421 327 891 1 236 880 892 418 566 616 4 065 Maximum 2 547 2 892 677 2 548 3 436 4 321 3 011 2 533 2 351 2 604 12 017 Quartile 25 % 1 531 1 472 360 1224 1 549 1 592 1 038 1 071 921 855 4 065 Quartile 75 % 2 389 2 039 652 1 592 3 244 3 537 2 531 1 914 1 539 1 453 12 017 Lower whisker 768 1 421 327 891 1,236 880 892 418 566 616 4 065 Upper whisker 2 547 2 892 677 2 548 3 436 4 321 3 011 2 533 2 351 2 604 12 017 Table 6. Economic land productivity value (thousands of$·ha-1) of 11 irrigation districts in the Río Bravo basin and nationwide, Mexico.
Year Irrigation district Nationwide
004 005 006 009 025 026 031 050 090 103 113
2002 21.85 8.14 14.47 4.52 6.04 13.17 13.71 18.05
2003 23.27 8.15 15.10 5.63 5.33 7.61 4.97 17.08 10.86 17.83
2004 36.18 35.62 9.12 15.65 9.55 8.24 4.18 7.63 15.32 15.19 22.19
2005 3.58 30.00 9.50 17.56 5.75 9.29 5.43 29.35 19.05 16.25 19.86
2006 6.97 9.70 5.03 15.60 21.01 15.43 20.80
2007 6.40 30.89 6.77 16.96 8.68 12.52 3.92 14.55 18.51 17.57 25.51
2008 8.73 38.53 5.95 19.42 11.68 14.23 8.83 27.48 13.45 24.76 28.89
2009 13.80 30.12 10.72 22.21 10.11 11.81 5.95 32.78 21.50 19.12 28.60
2010 17.89 35.72 10.64 28.96 11.23 11.32 6.78 51.24 24.53 21.76 30.71
2011 18.91 34.24 15.36 25.50 13.84 15.09 9.75 40.76 29.36 45.90 34.52
2012 17.86 39.76 12.14 25.57 17.97 25.76 11.95 52.21 27.12 40.79 42.36
2013 20.37 46.80 11.60 24.83 16.17 20.38 14.57 47.86 32.44 25.31 39.49
2014 16.26 40.50 13.38 32.32 15.50 23.24 11.12 51.45 34.26 22.33 61.68 37.97
2015 28.67 66.26 13.85 37.62 20.04 22.79 77.50 45.48 32.24 93.51 45.28
2016 34.66 81.13 13.95 38.27 18.61 22.74 10.35 83.96 54.91 34.61 110.53 51.48
Table 7. Descriptive statistics of land economic productivity (thousands of $·ha-1) of 11 irrigation districts in the Río Bravo basin, Mexico. Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 18.61 39.62 10.66 23.89 12.27 14.47 7.97 38.38 25.81 23.72 88.57 Median 17.87 35.67 10.68 23.52 11.46 12.52 7.19 36.77 21.50 21.76 93.51 Standard deviation 10.33 16.15 2.87 8.05 4.82 6.91 3.21 24.20 11.97 10.37 24.80 Minimum 3.58 21.85 5.95 14.47 5.63 4.52 3.92 4.97 13.17 10.86 61.68 Maximum 36.18 81.13 15.36 38.27 20.04 25.76 14.57 83.96 54.91 45.90 110.53 Quartile 25 % 9.99 30.09 8.15 16.63 8.25 9.29 5.33 15.34 17.08 15.43 61.68 Quartile 75 % 26.59 42.08 13.50 29.80 16.62 22.74 10.54 51.64 32.44 32.24 110.53 Lower whisker 3.58 21.85 5.95 14.47 5.63 4.52 3.92 4.97 13.17 10.86 61.68 Upper whisker 36.18 72.42 15.36 38.27 20.04 25.76 14.57 83.96 54.91 45.90 110.53 Table 8. Yield (t·ha-1) obtained for 11 irrigation districts in the Río Bravo basin and the nationwide value, Mexico. Year Irrigation district Nationwide 004 005 006 009 025 026 031 050 090 103 113 2002 12.30 23.05 16.24 4.13 6.09 11.44 14.17 15.24 2003 12.91 24.95 13.36 4.34 3.99 8.53 7.60 12.45 12.70 15.38 2004 14.29 12.32 22.84 13.12 6.09 9.36 3.57 18.28 12.18 10.08 17.30 2005 3.85 12.57 24.18 12.89 4.65 5.84 5.16 16.83 12.61 17.75 15.50 2006 4.69 5.40 5.14 11.12 13.65 20.31 15.83 2007 8.33 21.66 19.52 13.27 4.74 5.82 3.18 14.49 13.04 15.56 16.04 2008 4.81 19.98 16.40 13.06 4.53 5.02 6.44 25.15 9.53 17.04 16.06 2009 9.36 21.20 17.93 14.98 4.54 5.43 3.93 25.04 10.32 14.31 15.20 2010 10.53 20.80 18.98 15.60 5.28 4.99 4.86 31.95 12.58 8.36 15.47 2011 9.47 20.29 22.71 10.01 4.33 4.27 3.89 23.20 12.49 21.81 15.07 2012 9.13 26.97 21.48 19.83 5.29 5.96 5.46 27.93 47.92 43.41 17.70 2013 10.21 24.79 18.60 20.11 4.70 5.72 4.84 26.07 46.53 41.10 17.34 2014 9.13 27.66 19.96 19.81 5.30 6.45 4.28 25.14 42.51 31.65 15.17 16.40 2015 11.25 29.12 20.44 25.39 5.91 6.90 32.95 49.40 33.64 10.00 17.65 2016 13.76 41.39 21.58 24.25 5.95 6.83 3.89 33.15 47.88 34.13 9.20 18.27 Table 9. Descriptive yield measurements (t·ha-1) of 11 irrigation districts in the Río Bravo basin, Mexico. Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 9.51 21.71 20.90 16.57 5.02 5.74 4.95 22.78 23.64 22.40 11.46 Median 9.41 21.00 20.96 15.29 4.72 5.72 4.85 25.09 12.61 17.75 10.00 Standard deviation 3.03 8.13 2.49 4.61 0.61 1.35 1.40 8.04 17.08 11.40 3.24 Minimum 3.84 12.30 16.40 10.01 4.33 3.99 3.18 7.60 9.53 8.36 9.20 Maximum 14.29 41.39 24.95 25.39 6.09 9.36 8.53 33.15 49.40 43.41 15.17 Quartile 25 % 8.53 12.83 18.88 13.10 4.54 4.99 3.89 16.25 12.18 14.17 9.20 Quartile 75 % 11.07 27.14 22.89 19.90 5.46 6.45 5.62 28.93 46.53 33.64 15.17 Lower whisker 4.72 12.30 16.40 10.01 4.33 3.99 3.18 7.60 9.53 8.36 9.20 Upper whisker 14.29 41.39 24.95 25.39 6.09 9.36 8.53 33.15 49.40 43.41 15.17 Table 10. Economic productivity of water at level of the supply source ($·m-3) of 11 irrigation districts in the Río Bravo basin and nationwide, Mexico.
Year Irrigation district Nationwide
004 005 006 009 025 026 031 050 090 103 113
2002 1.09 0.82 0.85 0.77 0.60 0.70 0.76 1.3
2003 1.41 1.15 0.90 2.15 0.91 1.21 1.98 0.84 0.62 1.6
2004 12.01 2.07 2.19 1.11 2.31 1.77 0.36 3.21 1.13 0.91 1.8
2005 0.19 1.54 0.90 1.32 1.50 1.29 0.43 4.58 1.00 0.86 1.6
2006 1.59 1.31 0.59 3.05 1.25 1.00 1.6
2007 0.55 1.88 0.65 1.28 2.30 2.28 0.60 5.54 1.33 0.97 2.0
2008 0.55 2.71 0.50 1.49 2.12 1.85 0.76 8.65 0.83 1.85 2.2
2009 0.72 1.55 0.71 1.41 2.06 1.75 0.53 6.48 1.20 1.07 2.2
2010 1.26 2.15 1.44 1.78 3.23 2.60 0.92 8.21 1.37 1.62 2.5
2011 1.03 1.81 1.04 1.89 2.10 1.95 0.71 9.19 1.42 2.51 2.0
2012 1.27 2.34 1.09 1.85 3.28 3.57 1.08 12.69 2.03 2.59 3.9
2013 1.27 3.23 1.07 1.74 4.68 3.32 1.64 12.60 2.38 1.68 3.7
2014 1.00 2.72 0.94 2.49 5.72 4.81 2.00 8.98 2.33 1.47 2.82 3.5
2015 1.79 4.58 1.63 2.36 7.49 7.52 20.09 2.72 1.84 4.47 3.7
2016 1.62 5.89 1.25 2.53 5.28 4.71 2.23 22.29 3.40 2.31 6.07 4.0
Table 11. Descriptive statistics of the economic productivity of water at level of the supply source ($·m-3) of 11 irrigation districts in the Río Bravo basin, Mexico. Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 1.94 2.50 1.10 1.64 3.27 2.70 0.98 9.11 1.59 1.47 4.45 Median 1.15 2.11 1.05 1.61 2.31 1.95 0.74 8.43 1.33 1.47 4.47 Standard deviation 3.20 1.32 0.44 0.55 1.82 1.83 0.59 6.09 0.79 0.65 1.63 Minimum 0.19 1.09 0.50 0.85 1.50 0.77 0.36 1.98 0.70 0.62 2.82 Maximum 12.01 5.89 2.19 2.53 7.49 7.52 2.23 22.29 3.40 2.59 6.07 Quartile 25 % 0.59 1.55 0.79 1.24 2.09 1.31 0.57 4.24 1.00 0.91 2.82 Quartile 75 % 1.53 2.85 1.30 2.01 4.83 3.57 1.32 12.63 2.33 1.85 6.07 Lower whisker 0.19 1.09 0.50 0.85 1.50 0.77 0.36 1.98 0.70 0.62 2.82 Upper whisker 3.55 5.48 2.19 2.53 7.49 7.52 2.23 22.29 3.40 2.59 6.07 Table 12. Water productivity at the level of the supply source (kg·m-3) of 11 irrigation districts in the Río Bravo basin and nationwide, Mexico. Year Irrigation district Nationwide 004 005 006 009 025 026 031 050 090 103 113 2002 0.62 2.33 0.95 0.70 0.60 0.61 0.78 0.99 2003 0.78 3.51 0.80 1.65 0.68 1.36 3.04 0.61 0.73 1.23 2004 4.74 0.72 5.48 0.93 1.47 2.01 0.30 7.69 0.90 0.60 1.18 2005 0.21 0.65 2.28 0.97 1.21 0.81 0.41 2.63 0.66 0.94 1.09 2006 1.07 0.73 0.60 2.17 0.81 1.32 1.07 2007 0.72 1.32 1.89 1.00 1.26 1.06 0.48 5.52 0.94 0.86 1.14 2008 0.30 1.40 1.38 1.00 0.82 0.65 0.56 7.92 0.59 1.27 1.09 2009 0.49 1.09 1.19 0.95 0.92 0.80 0.35 4.95 0.58 0.80 1.01 2010 0.74 1.25 2.57 0.96 1.52 1.15 0.66 5.12 0.71 0.62 1.13 2011 0.52 1.07 1.54 0.74 0.66 0.55 0.28 5.23 0.60 1.19 0.76 2012 0.65 1.59 1.93 1.43 0.96 0.83 0.49 6.79 3.59 2.75 1.48 2013 0.63 1.71 1.71 1.41 1.36 0.93 0.54 6.87 3.41 2.72 1.43 2014 0.56 1.86 1.40 1.53 1.96 1.34 0.77 4.39 2.89 2.08 0.69 1.28 2015 0.70 2.02 2.41 1.59 2.21 2.28 8.54 2.95 1.91 0.48 1.26 2016 0.64 3.00 1.93 1.60 1.69 1.41 0.84 8.80 2.96 2.28 0.51 1.27 Table 13. Descriptive statistics of water productivity at level of supply source (kg·m-3) of 11 irrigation districts in the Rio Bravo basin, Mexico. Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 0.91 1.36 2.25 1.13 1.34 1.06 0.59 5.69 1.52 1.39 0.56 Median 0.64 1.28 1.93 0.98 1.31 0.83 0.55 5.37 0.81 1.19 0.51 Standard deviation 1.22 0.65 1.11 0.31 0.44 0.51 0.27 2.17 1.22 0.76 0.12 Minimum 0.20 0.62 1.19 0.74 0.66 0.55 0.28 2.17 0.58 0.60 0.48 Maximum 4.74 3.00 5.48 1.60 2.21 2.28 1.36 8.80 3.59 2.75 0.69 Quartile 25 % 0.49 0.76 1.50 0.95 0.95 0.70 0.40 4.05 0.61 0.78 0.48 Quartile 75 % 0.71 1.75 2.45 1.46 1.66 1.34 0.69 7.75 2.95 2.08 0.69 Lower whisker 0.20 0.62 1.19 0.74 0.66 0.55 0.28 2.17 0.58 0.60 0.48 Upper whisker 1.47 3.00 4.35 1.60 2.21 2.28 1.30 8.80 3.59 2.75 0.69 Table 14. Water economic productivity at user level ($·m-3) of 11 irrigation districts of the Rio Bravo basin, Mexico.
Year Irrigation district
004 005 006 009 025 026 031 050 090 103 113
2012 2.64 3.73 2.76 3.14 6.77 5.94 1.51 16.40 3.62 4.02
2013 3.06 6.87 2.92 3.41 8.41 5.21 2.18 16.28 4.32 2.66
2014 2.43 4.70 3.00 4.23 10.32 7.33 2.32 11.60 4.48 2.10 4.42
2015 3.79 6.92 5.70 3.89 16.59 11.85 27.47 5.34 3.21 7.56
2016 3.50 8.65 3.42 4.10 10.38 6.95 2.48 28.80 6.67 3.56 9.28
Table 15. Descriptive statistics of economic water productivity at the user level ($·m-3) of 11 irrigation districts in the Río Bravo basin, Mexico. Statistics Irrigation district 04 05 06 09 025 026 031 050 090 103 113 Average 3.09 6.18 3.56 3.75 10.50 7.46 2.12 20.11 4.88 3.11 7.08 Median 3.06 6.87 3.00 3.89 10.32 6.95 2.25 16.40 4.48 3.21 7.56 Standard deviation 0.57 1.96 1.22 0.46 3.72 2.59 0.43 7.59 1.17 0.76 2.47 Minimum 2.43 3.73 2.76 3.14 6.77 5.21 1.51 11.60 3.62 2.10 4.42 Maximum 3.79 8.65 5.70 4.23 16.59 11.85 2.48 28.80 6.67 4.02 9.28 Quartile 25 % 2.54 4.22 2.84 3.28 7.59 5.58 1.67 13.94 3.97 2.38 4.42 Quartile 75 % 3.65 7.79 4.56 4.17 13.49 9.59 2.44 28.14 6.00 3.79 9.28 Lower whisker 2.43 3.73 2.76 3.14 6.77 5.21 1.51 11.60 3.62 2.10 4.42 Upper whisker 3.79 8.65 5.70 4.23 16.59 11.85 2.48 28.80 6.67 4.02 9.28 Table 16. Water productivity at user level (kg·m-3) of 11 irrigation districts of the Rio Bravo basin, Mexico. Year Irrigation district 004 005 006 009 025 026 031 050 090 103 113 2012 1.35 2.53 4.88 2.44 1.99 1.38 0.69 8.77 6.39 4.28 2013 1.54 3.64 4.68 2.76 2.45 1.46 0.72 8.87 6.20 4.32 2014 1.37 3.21 4.47 2.59 3.53 2.03 0.89 5.67 5.55 2.97 1.09 2015 1.49 3.04 8.42 2.62 4.90 3.59 11.68 5.80 3.35 0.81 2016 1.39 4.41 5.28 2.60 3.32 2.09 0.93 11.37 5.82 3.51 0.77 Table 17. Descriptive statistics for water productivity at the user level (kg·m-3) of 11 irrigation districts in the Río Bravo basin, Mexico Statistics Irrigation district 004 005 006 009 025 026 031 050 090 103 113 Average 1.43 3.37 5.55 2.60 3.24 2.11 0.81 9.27 5.95 3.69 0.89 Median 1.39 3.21 4.88 2.60 3.32 2.03 0.81 8.87 5.82 3.51 0.81 Standard deviation 0.08 0.71 1.63 0.11 1.12 0.89 0.12 2.43 0.34 0.59 0.17 Minimum 1.35 2.53 4.47 2.44 1.99 1.38 0.69 5.67 5.55 2.97 0.77 Maximum 1.54 4.41 8.42 2.76 4.90 3.59 0.93 11.68 6.39 4.32 1.09 Quartile 25 % 1.36 2.79 4.58 2.52 2.22 1.42 0.70 7.22 5.67 3.16 0.77 Quartile 75 % 1.51 4.03 6.85 2.69 4.21 2.84 0.92 11.52 6.30 4.30 1.09 Lower whisker 1.35 2.53 4.47 2.44 1.99 1.38 0.69 5.67 5.55 2.97 0.77 Upper whisker 1.54 4.41 8.42 2.76 4.90 3.59 0.93 11.68 6.39 4.32 1.09 Table 18. Average values of the seven indicators evaluated per irrigation district in the Río Bravo basin and nationwide, Mexico. Indicator Irrigation district Nationwide 004 005 006 009 025 026 031 050 090 103 113 (1) RAP ($·t-1) 1834 1864 514 1460 2416 2519 1684 1544 1345 1191 8479 1875.7
(2) EPL (thousand $·ha-1) 18.61 39.62 10.66 23.9 12.27 14.47 7.97 38.4 25.8 23.72 88.6 30.9 (3) Yield (t·ha-1) 9.51 21.71 20.9 16.6 5.02 5.74 4.95 22.8 23.6 22.4 11.5 16.3 (4) EPWf ($·m-3) 1.94 2.5 1.1 1.64 3.27 2.7 0.98 9.11 1.59 1.47 4.45 1.17
(5) WPf (kg·m-3) 0.91 1.36 2.25 1.13 1.34 1.06 0.59 5.69 1.52 1.39 0.56 0.99
(6) EPWu ($·m-3) 3.09 6.18 3.56 3.75 10.5 7.46 2.12 20.1 4.88 3.11 7.08 - (7) WPu (kg·m-3) 1.43 3.37 5.55 2.6 3.24 2.11 0.81 9.27 5.95 3.69 0.89 - Table 19. Average values of the distribution of seven performance indicators of 11 irrigation districts (ID) in the Río Bravo basin, Mexico (from 2002 to 2016) Indicator Average Reference range Intermediate Low High (1) RAP ($·t-1) 2 259.09 514 (ID 006) 8 479 (ID 113) 325 - 16 572
(2) EPL (thousand $·ha-1) 27.63 7.97 (ID 031) 88.57 (ID 113) 8.8 - 226.0 (3) Yield (t·ha-1) 14.97 4.95 (ID 031) 23.64 (ID 090) 4.4 - 102.6 (4) EPWf ($·m-3) 2.80 1.1 (ID 006) 9.11 (ID 050) 0.38 - 20.3
(5) WPf (kg·m-3) 1.62 0.56 (ID 113) 5.7 (ID 050) 0.50 - 26.2
(6) EPWu (\$·m-3) 6.53 2.12 (ID 031) 20 (ID 050) 1.0 - 21.47
(7) WPu (kg·m-3) 3.54 0.89 (ID 113) 9.27 (ID 050) 0.75 - 37.1
The data in brackets indicates the irrigation district with the highest or lowest average value. The reference column is based on the study of Altamirano-Aguilar et al. (2017).
Table 20. Analysis of water productivity dispersion at level of the supply source (WPf) per irrigation district (IDs) analyzed.
ID WPf Highlights
004 It has outliers of 0.21 and 4.74 kg·m-3. In 2016, it had a productivity of 0.64 kg·m-3, which is equal to the Median.
005 It has upward values and Upper Whisker limits of 3 kg·m-3.
006 Part of high values. In 2016, it had a productivity of 1.93 kg·m-3, which was lower than in 2015.
009 It shows an increase since 2009, with the highest value in 2016 of 1.60 kg·m-3.
025 It shows ups and downs greater than the Median (1.31 kg·m-3), with a Maximum of 2.21 kg·m-3 in 2015. In the period evaluated it showed an average of 1.34 kg·m-3.
026 Values oscillate mainly in the range of 0.65 to 1.4 kg·m-3, with an outlier Maximum value of 2.28 and an average value of 1.06 kg·m-3.
031 It shows little variation in values, with a small positive trend in the analysis period and a high outlier of 1.36 kg·m-3 in 2003.
050 It starts with high values, and during the period evaluated shows values higher than 7.75 kg·m-3 and a Median of 5.37 kg·m-3. In 2016 it had the highest productivity of all the IDs, with a value of 8.80 kg·m-3.
090 It started with low values, and from 2012 productivity increased above the average and Median, with an outlier of 3.59 kg·m-3.
103 It starts with low values, and from 2012 productivity increased above the average and Median, with an outlier of 2.75 kg·m-3.
113 It has very few available data. In 2016 it had values equal to the Median (0.51 kg·m-3).
Table 21. Conduction efficiencies of 11 irrigation districts in the Rio Bravo basin, Mexico
Year Irrigation districts
004 005 006 009 025 026 031 050 090 103 113
2012 0.48 0.63 0.39 0.59 0.48 0.6 0.72 0.77 0.56 0.64
2013 0.41 0.47 0.37 0.51 0.56 0.64 0.75 0.77 0.55 0.63
2014 0.41 0.58 0.31 0.59 0.55 0.66 0.86 0.77 0.52 0.7 0.64
2015 0.47 0.66 0.29 0.61 0.45 0.63 0.73 0.51 0.57 0.59
2016 0.46 0.68 0.37 0.62 0.51 0.68 0.9 0.77 0.51 0.65 0.65