Irrigation, Irrigation System, and Irrigation Scheme

Agricultural irrigation is a complex mixture of technical, institutional, economic, social, and environmental processes that has been conceptualized in various manners. ^{Chambers (1988)} identifies irrigation as a scheme consisting of physical, human, and bio-economic domains; among which exchanges of goods and services take place. Using the systemic approach, ^{Small & Svendsen (1990)} consider irrigation as a system, with inputs, outputs, and effects. The system itself is considered to be within a context of embedded economic systems. Following the systemic approach, ^{Burton (2010)} suggests that irrigation should be studied as a system consisting of 5 domains, which are shown in Table 1.

Irrigation System and Irrigation Scheme

For the study of irrigation management, from a administrative perspective, it is important to clarify two concepts: Irrigation System, and Irrigation Scheme. An irrigation system refers to the network of irrigation and drainage canals, including their structures. Irrigation scheme refers to the total irrigation and drainage complex, the irrigation system, the irrigated land, the towns, roads, etc. (^{Burton, 2010}).

Performance Evaluation in an irrigation scheme: general framework

The general framework, proposed by ^{Burton (2010)}, to develop a performance evaluation program in an irrigation scheme consists, operationally, of 4 general stages: Purpose and Scope, Design, Implementation and Action. Each stage is described briefly below.

Evaluation Levels

Performance evaluation can be done at different levels. At the sector level when irrigation is evaluated in terms of its performance in comparison to other uses for water resources. At the main system level, where the performance of the delivery service for water is measured. At the farm level, where the performance of water delivery to the farm, the use of water, and the application of water is measured. At the irrigation scheme level, where individual scheme performance is measured, implicitly or explicitly, against its established objectives; or when performance is measured for different schemes against themselves. It is important to define from the start if performance evaluation is for a scheme (internal analysis), or to compare between schemes (external analysis). A significant problem with performance analysis for irrigation schemes is the complexity, and the great variety of existing scheme types. This makes comparisons among them difficult. For example, the irrigation schemes can have different forms of management, irrigation technology, etc. There is no existing methodology yet that provides a definitive approach to categorize irrigation schemes. For this reason, discussion continues to be present regarding comparisons among equal entities. Key descriptors for irrigation schemes can be used as a starting point to select schemes with similar key features for comparison. However, at this point it is important to recognize that comparison among different types of schemes can be equally valuable.

Benchmarking

Benchmarking of irrigation schemes is a comparative way (external) of evaluating performance that has been frequently used. Generally, benchmarking seeks to compare the performance of the schemes with “best practices” against schemes of lower performance, and identify differences in performance (^{Burton, 2010}). A manner in which to do benchmarking is by comparing the technical efficiency of organizations under study, when doing their activities.

Technical Efficiency Analysis

The analysis of technical efficiency can be done through different statistical and mathematical tools. DEA is a linear programing technique, which has been used successfully to evaluate the relative performance of a set of organizational units that use the same resources (inputs), and obtain the same results (outputs) (^{Ramanathan, 2003}; ^{Zhu, 2010}). The organizational units of interest are called Decision Making Units (DMU). The main goal of DEA is to measure the efficiency in the use of the available resources by the DMUs to generate a set of products (^{Charnes, Cooper & Rhode, 1979}). Through DEA, the performance of the DMUs is evaluated in terms of technical efficiency, which corresponds to a relative value that relates outputs with respect to inputs in the DMUs (^{Ramanathan, 2003}). A brief description of the more commonly used DEA models for benchmarking studies is presented below.

Returns to Scale

For a better understanding of the performance of a DMU, in addition to DEA efficiency, is important to determine its return to scale. In general, a DMU may have decreasing, constant, or increasing return to scale. The return to scale is decreasing when a proportional increase in inputs produce a smaller proportion of increase in outputs; it is constant when the proportions are equal; and it is increasing when a proportion of increase in inputs produce a larger proportion of increase in outputs. Figure 1 shows technical efficiency, scale efficiency, and the 3 types of returs to scale for DMUs with one input and one output.

Figure 1 Returns to Scale. Adapted from ^{Malana and Malano (2006)}. 

Under the CCR model, if (u*, v*) are optimal solutions, then cu*, cv* are also optimal solutions, for all constant c>0. Therefore, under a CCR model, an optimal DMU performs in a constat return to scale. In practice this is a very restrictive condition, since most of the DMUs perform under a variable return to scale. The BCC model is an improvement over the CRR model, since it includes variable return to scale by incorporating the restriction ∑i=1nλi=1 to CCR model, which corresponds to a convex efficiency frontier, allowing to identify whether a DMU has an increasing, constant, or decreasing return to scale (^{Cooper, Seiford & Tone, 2007}).

Tobit Regression

Once efficient and inefficient DMUs have been determinated by DEA, the next step is to identify which factors are causing innefficiency. One way to do so consists in relating the efficiency values with variables that influence on the operation of the DMUs. The relative nature of the technical efficiency estimated makes it a censored dependent variable, so that Tobit regression is recommended in this case. A Tobit model with two limits is suitable to estimate the variable and efficiency indicator’s impacts on efficiency, since efficency values are censored between 0 and 1 (^{Maddala, 1986}).

The expression of the Tobit model is:

where, yi* is a latent variable that represents the efficiency value for DMU _i ; β₀ and β_m are unknown parameters that have to be estimated; xim = 1,2,…, M are explicative (independent) variables associated with DMU _i ; and εi = independent normal distributed error terms with zero mean and constant variance, σ². The latent variable yi* is expressed in terms of the observed variable y_i (the efficiecy result obtained using DEA analysis) in the following form:

Step 1: Purpose and scope

The results of this work will be useful for central management and ID managers, as well as, researchers interested in water irrigation management. The evaluation adresses the farm producers and irrigation managers point of view and was carried out by a group of researchers and graduate students at CIAD, AC.

The type of evaluation is operational by schemes (IDs), specifically defined by the physical and geographical frontiers of each ID and temporally by the 2011-2012, 2012-2013 and 2013-2014 agricultural seasons. The scope of the performance evaluation, based on the nested system proposed by ^{Small & Svendsen (1990)}, comprehends the irrigation system, the agricultural irrigation system, and agricultural economic system.

The purpose of this work is to contribute to the improvement of ID management. The general objective is to increase agricultural and economical water productivity, through the following specific objectives: (1) maximize the amount of distributed water, (2) maximize the income from water service fees, (3) maximize agricultural and economical water productivity, and (4) reduce the impact of irrigated agriculture activities on soil degradation.

Step 2: Design

From the objectives of the performance evaluation, the criteria and performance indicators shown in Table 3 were defined. To compute performance indicators, values of the following variables from each ID, were used: Total chanel´s length (km), Restoration costs ($), Technification costs ($), Efficiency of water conduction, Volume of total water delivered to users (thousands of m³), Total irrigated area (ha), Agricultural production (thousands of tons), Management costs (thousands of $), Operation costs (thousands of $), Maintenance costs (thousands of $) and a Soil degradation index.

For the efficiency and productivity analysis, the input oriented DEA CCR and BCC models were implemented using performance variables and indicators under the systemic model proposed by ^{Malano & Burton (2001)} for an irrigation scheme, which includes three domains: (1) Delivered service (which includes the areas of System Operation and Financial Performance), (2) Productive efficiency and (3) Environmental Performance.

To apply DEA analysis the following systems were considered: Infrastructure (I) in the area of system operation, General Finances (FG) in the area of financial performance, General Production (PG) in productive efficiency and Environmental (E) in the environmental performance. Relative efficiencies, returns to scale, IDs with the best performances (efficient IDs), and comparisons of IDs with low performance (inefficient IDs) were determined based on the DEA results.

Step 3: Implementation

Data collection depended on availabilty of records at goverment agencies. Agricultural and hydrometric data were obtained from the Estadísticas Agrícolas de Distritos de Riego for the agricultural seasons: 2011-2012, 2012-2013 y 2013-2014 (^{Conagua, 2015a}). Financial records on hydraulic infrastructure were obtained from ^{Conagua (2014b}, ^2015b) and the ^{Subdirección General de Infraestructura (2013)} Data validation was confirmed by descriptive statistical techniques. The relative efficiency analysis was carried out for the models shown in Table 4, using the DEA software OSDEA-GUI, Version 0.2.

Returns to scale were determined according to the method proposed by (^{Banker, Cooper, Seiford & Zhu, 2011}) using the values of efficiency for the CCR and BCC models, and the values of 𝑗 𝑛 𝜆 ∗ 𝑗 obtained from the CCR model. First, all IDs with the same CCR and BCC efficiencies were chosen, independently of the values for ∑jnλ*j obtained from the CCR model. These IDs have constant return to scale (CRS). Next, for any CCR efficiency result, the return rates were determined for each one of the remaining IDs. If ∑jnλ*j <1, the ID shows increasing return to scale. If ∑jnλ*j >1, the ID shows decreasing return to scale.

Tobit regression, with two limits, was applied with efficiency as the dependent variable, and as independent variables: Irrigared area (IA) (ha), Number of users (NU), Covered chanels (CC) (%), Uncovered chanels (CSR) (%), Total annual production/irrigated area (TAP/IA) (ton/ha), Production value/Irrigated area (PV/IR) (thousands of $/ha), Maintenance cost /Irrigated area (CM/IA) (thousands of $/ha), and Soil degradation index (SDI). The statistical analysis was carried out using the Stata 14 software.

Benchmarking

Because of space restrictions, benchmarking analysis is presented only for clusters CS5 (IDs 50, 23, 31, 85, 76, 4, 83, 86, 26, 42, 97 and 34) and CS6 (IDs 52, 108, 74, 10, 109, 75 and 63).

Cluster CS5 showed large variability in irrigated area and number of users, eventhough its statistics exhibit that its IDs are of median size. On the other hand, its IDs are homogeneous in infrastructure, volume and production value, maintenance cost, soil degradation, and supply and conducting source. By main crop volume, this cluster is composed of forage producer IDs (Table 4).

The statistics for irrigated area and number of users show that the Cluster CS6 is composed of large IDs. The IDs are homogeneous in infrastructure, volume and value of production, maintenance cost, soil degradation, and source of supply and conduction. By the volumes of its main crops, this cluster is composed by corn and vegetables producer IDs (Table 5).

Benchmarking for Cluster CS5. Input oriented DEA efficency analysis was conducted using the input-output variables and indicators shown in Table 6.

The Cluster CS5 had a mean efficiency e = 0.73, with a prevailing increasing return to scale. To reach the BCC efficiency frontier, maintaining high output levels, the IDs should reduce their input levels. Furthermore, the IDs showed increasing return to scale, allowing them to increase their productivity and/or to reach a constant return to scale by increasing thier productive capacity (Table 7).

In infrastructure, the mean group efficiency was low (e = 0.54). In particular, the IDs 50, 23, 31, 85 and 4 used all their resources efficiently; while the the IDs 76, 83, 86, 26, 42, 97 and 34 used their resources excessively, having large rehabilitation and technification costs for the efficiency level of conduction shown.

In General Finances, the mean efficiency was high (0.95), prevailing constant and/or incresing returns to scale. In general, the income from fees for water services was sufficient to cover the IDs management, operation, and rehabilitation costs.

In General Production, the group mean efficiency was regular (e = 0.73), prevailing an incresing return to scale. The volume of delivered water and irrigated area were high for the volumes and values of production given. ID 50 used completely and efficiently its delivered water and irrigated area for the volume and value of production shown. The IDs 23 and 31 should change to a constant return to scale, by increasing the volume and value of their production through better agricultural practices, or introducing high output and value crops. The remaining IDs should reduce their water loses, introduce better agricultural practices or look for crops of larger yield and value.

In the Environmental system the mean efficiency was regular (e = 0.70), prevailing an increasing return to scale. With exception of IDs 50 and 4, in general, most of the IDs showed high levels of soil degradation, which affects their agricultural production (Table 7).

Comparatively, ID 50 is the most efficient and its practices can be reference criteria for the whole cluster. ID 31 emerged as a referent in Infrastructure and General Finances for IDs 85, 76, 4, 83, 86, 26, 42, 97 and 34. In terms of mean general efficiency, ID 50 was the best evaluated (e = 1.0) and ID 34 was the worst evaluated (e = 0.454). The IDs in this group were ranked according to their mean efficiency (Table 8).

Tobit regression analysis showed that Irrigated area (p = 0.010), Covered chanels (p = 0.001), Uncovered chanels (p = 0,001), Annual total production/irrigated area (p = 0.010), Value of production/irrigated area (p = 0.003), and Maintenance costs/Irrigated area (p = 0.002) were significant factors for the level of mean efficiency of the IDs that conform Cluster CS5 (Table 9).

Benchmarking of Cluster CS6. This cluster showed a global mean efficiency e = 0.88, indicating an inappropriate use of resources. However, since no return to scale turned out to be predominant, it was not possible to establish general recommendations for this cluster in terms of use of resources and changes in return to scale (Table 10).

In infrastructure, Cluster CS6 had a regular average efficiency (e = 0.75). Particularly, the IDs 52, 108, and 74 used all their resources efficiently. The IDs 109, 75, and 63 had excesive rehabilitation and technification costs asociated with low efficiency on water conduction. ID 10 was BCC efficient, but presented decreasing return to scale, therefore, it would have to look over its rehabilitation and technification activities, as well as, to review its water conduction practices.

The General Finances of this cluster presented a high average efficiency (e = 0.96). Collection from fees for water services were sufficient to cover management, operation, and maintenance activities. Only ID 10 was inefficient with an increasing return to scale. Consequently, it would have to reduce its management, operation, and conservation costs.

In General Production, the average group efficiency was high (e = 0.94) with a constant return to scale. The IDs 52, 108, 10, and 109 had optimal volume and value of production in relation to the volume of water received and the irrigated area. ID 75 was inefficient with decreasing return to scale. It would have to increase its volume and value of production by implementing better agricultural practices and introducing high value crops. ID 63 was inefficient with increasing return to scale and it has to reduce water distribution losses.

In the Environmental system the group had good average efficiency (e = 0.85) and heterogeneus return to scale. ID 109 was efficient, with no soil degradation effect on its crop production. ID 52 was efficient, but it may change its return to scale by improving soil quality through better agricultural practices (Table 10).

Comparatively, ID 52 is the most efficient and its practices may constitute reference criteria in Genaral Finances and Environmental for the 108, 10, 63, 52 , and 75. In Infrastructure, IDs 74 and 108 can be referents for IDs 109, 75, and 63. In General Production, ID 10 was a referent for IDs 75 and 63. In terms of general mean efficiency, ID 51 was the best evaluated (e = 1.0) and ID 63 was the worst evaluated (e = 0.69). It is possible to rank the IDs in Cluster CS6 in terms of mean efficiencies (Table 11).

According to the Tobit regression results, Soil Degradation Index was the only independent variable significantly (p - 0. 054) related with efficiency for this cluster (Table 12).