Temporal similarity of the mechanization level and crop yield in Eritrea

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Background

Agriculture relies on a diverse range of input resources for successful and efficient production, in addition to essential cultivation environment, including power sources (humans, animals, and/or machines) [1]. Agricultural production has progressively advanced toward a highly mechanized state, striving to maximize output with fewer resources [2–6].The level of mechanization (LOM) can be measured by the extent to which mechanical power is used in the agricultural sector. One common LOM indicator is the horse power (hp) per thousand hectares of cultivated land [3, 4].

This metric varies over time, particularly in low-income countries, reflecting the influence of prevailing socioeconomic, governmental, and other factors. Although technological advancements offer cost-effective and efficient machines, agricultural sectors can be sensitive to investments in mechanization during economic fluctuations (growth or recession) [5–8]. This progression of LOM could exhibit periodic trends, influenced by a complex interaction of socioeconomic, environmental, and policy factors that may fluctuate over time [9], leading to corresponding variations in the agricultural production and productivity. This can be treated as a time series problem, and the similarities in the pattern of the fluctuations between the two sequences can be assessed using the ordinary least square (OLS) and the dynamic time warping (DTW) methods.

OLS is a versatile, widely used technique for establishing statistical relations between parameters. Sharma et al. (2011), Larrabee et al. (2014), and Sharma et al. (2013) have used the OLS to analyze the relationships between crop yields and influencing factors such as average precipitation [10], soil properties, management practices [11], and product quality and influencing factors [11]. OLS is useful for analyzing economic factor effect [12], quantifying the effect of farm machinery on crop yield, identifying the determinants of farm machinery adoption, examining the relationship between the use of machinery and input resources, and assessing farm machinery investment feasibility and profitability. It also enhances input management tactics and assesses the combined impact of equipment adoption and off-farm employment on farm performance [13]. However, it lacks precision in analyzing the temporal patterns of time series datasets.

The DTW is particularly effective in comparing sequences of similar patterns but differing in timing, alignment, or length, and finding their optimal alignment [14–17]. In 1978, Sakoe applied the DTW optimization algorithm to recognize spoken words [16]. The DTW algorithm can also be used for automatic speech-to-lip alignment [18, 19], fingerprint matching validation [20], and facial and eye detection. It can be used for comparing, aligning, and combining time series sequences across comparable [17, 19] or incomparable spaces in multivariate time series classification [21]. DTW also facilitates similarity analysis between two sequences of datasets with temporal variability — whether shifted, scaled, or globally invariant [15] — and supports data mining for determining averages and indexing [22].

In agriculture, DTW is useful for measuring similarities between two temporal sequences for land use and land cover classification and mapping [23], for weighted derivative modification of DTW in crop mapping [24–26], for determining the temporospatial characteristics of agricultural non-point source pollution loads, and for identifying dominant processes and influencing factors.

The LOM is a significant determinant of production and productivity [8]. In Eritrean agriculture, particularly in cereal production, the LOM’s modest growth and volatility may contribute to the insignificant growth trend over the years. To examine the LOM’s effect on production, similarity analysis can be conducted using time series records of the LOM and yield. However, few studies have examined the similarity between cereal production and LOM time series datasets, both globally and in Eritrea, particularly through DTW. Eritrean cereal production varies over the years with mild growth, similar to the LOM. However, no scientific evidence establishes this relationship, effect, dependence, or similarity in pattern between these datasets.

Study Aim

This study analyzes the similarity between cereal production (yield) and the level of mechanization (LOM) in Eritrean agriculture to examine LOMs impact on crop yield using ordinary least squares (OLS) regression method for trend analysis and DTW for pattern similarity evaluation. By analyzing the temporal pattern similarity between yearly crop yields and LOM fluctuations, this study evaluates the influence of LOM on agricultural productivity.

Materials and methods

Assessment of the LOM

Power availability per unit area serves as a fundamental parameter in evaluating the extent of mechanization in agricultural systems. Accordingly, the LOM in kW/ha (hp/ha), as a function of mechanical power available in a farm, is given by equation 1 [4]:

$LOM=\sum _{i=0}^n\frac{P_i}{L_i}$, (1)

where P_i is the machinery power (kW or hp) and L_i is the total cultivated area (ha).

According to the United States department of agriculture (USDA), the LOM data for countries worldwide from 1961 to 2020 is available online in an interactive format [27], allowing users to inspect the LOM for each year within that range. A freely available CSV file containing diverse, extensive data, part of which is the total horsepower (in multiples of 1000 hp) of farm machinery in each country for specific years, is provided. These data were used to determine the LOM in this study, with the corresponding year’s cultivated area (in multiples of 1000 ha) obtained from the Eritrean Ministry of Agriculture.

Similarity analysis

A comprehensive multistep analysis was conducted to examine the similarity between the LOM and yield. First, we used OLS regression with an interaction term for preliminary time series trend similarity analysis and, second, we used a comprehensive analysis using DTW with robust similarity metrics. This approach clarifies the temporal relationship between the LOM and yield. The analysis was conducted in Python using appropriate libraries and packages. To address the different scales of datasets, the yield dataset was standardized and scaled simultaneously to match the LOM using equation 2 [28]:

$Y_s=\frac{Y-\overline{Y}}{{\sigma }_Y}\times {\sigma }_x+\overline{x}$, (2)

where Y_s is the standardized yield;  s the mean of the yield; σ_Y is the yield standard deviation; σ_x is the LOM standard deviation; and  is the LOM mean.

Ordinary Least Squares (OLS) Regression

The dependent and independent variables were modeled using OLS regression with an interaction term: Interaction = Year_Centered × (Standardized Yield not NA). “LOM” and “Standardized Yield” using first combined before configuring the regression model as [32]:

$y={\beta }_0+{\beta }_1\times Year\_Centered+{\beta }_2\times Interaction+\epsilon$. (3)

Dynamic Time Warping Distance Similarity Analysis

DTW aligns two datasets using dynamic programming to estimate local costs. For two multivariate time series sequences, the standard DTW formulation (equation 4) analyzes the time series  and , where T_x and T_y represent the sequential duration of the respective time series. Both sequences must have the same dimension p [15]:

$DTW=\min \sum _{\pi \in A(i,j)(i,j)\in \pi }^{n}d(x_i-y_i)$, (4)

where A (i, j) is the set of all permissible alignments between x and y. For most instances, the ground metric d is defined as d(x_i, y_j) = ‖x_i – y_j‖². To efficiently estimated similarity, we use dynamic programming based on the formulation in (equation 4) [14, 15, 21, 30]:

$DTW(x_{\to t_1},y_{\to t_2})=d(x_{t_1},y_{t_2})+\min \left\{\begin{array}{l}DTW(x_{\to t_1},y_{\to t_2-1})\\ DTW(x_{\to t_1-1},y_{\to t_2})\\ DTW(x_{\to t_1-1},y_{\to t_2-1})\end{array}\right.$, (5)

where  represents the time series x observed up to time t.

The distance matrix of datasets X = {x₁, x₂, …x_n} and X = {y₁, y₂, …y_m} with lengths n and m, aligned using DTW, is derived from the information contained in the n×m matrix as:

$distMatrix=\left(\begin{array}{ccc}{\text{d(x}}_{\text{1}}{\text{,y}}_{\text{1}}{\text{) d(x}}_{\text{1}}{\text{,y}}_2\text{)}& \text{…}& d(x_1,y_m)\\ ⋮& \ddots & ⋮\\ {\text{d(x}}_{\text{n}}{\text{,y}}_{\text{1}}{\text{) d(x}}_n{\text{,y}}_2\text{)}& \cdots & d(x_n,y_m)\end{array}\right)$, (6)

where distMatrix (i, j) is the distance of point i on X and point j on Y, and 1 ≤ i ≤ n and 1 ≤ j ≤ m. The DTW aims to discover the warping path π = {π₁, π₂, . . ., π_K} of the adjoining elements that minimizes the cost function.

DTW Algorithm

Input: Two sequences to be aligned: X = {x₁, x₂, …x_n} and X = {y₁, y₂, …y_m} and num_iterations (default is 1) and Output: optimal_path => similarity_score.

Algorithm Steps:

1. Data Alignment: No preprocessing is required as sequences are assumed to be aligned.
2. Dynamic Programming: Initialize a cumulative cost matrix A with size (m + 1) x (n + 1), where m and n are the lengths of x and y, respectively, and initialize all cells of the matrix with infinity values except for the top-left cell, A [0,0].

For each cell A[i, j] in the matrix: local cost = = |X[i] – Y[j]| => Update X[i] and Y[j] as A[i, j] = = local_cost + min A[i – 1, j], A[i, j – 1], A[i – 1, j – 1].

3. Optimal Path Extraction: Initialize an empty list optimal path => start from A [m − 1, n − 1] (bottom-right corner) =>trace back to the top-left corner A [0,0].
4. Similarity Measurement => similarity score => plot for visualization.

Evaluation of DTW distance similarity performance

To measure the similarity between yield and LOM, we used the following DTW distance parameters: mean, minimum, maximum, standard deviation, mean absolute error (MAE) and root mean square error (RMSE). A combination of these metrics was used to measure the level of similarity between the time series datasets, with lower values reflective of a better degree of similarity, and vice versa.

Result

The LOM of the country for a specific year is determined by dividing the total available horsepower in that year by the yearly cultivated area. The crop yield and the LOM over the years are shown in Fig. 1. The yield followed a pattern similar to the LOM, although decreases and increases varied, except in certain years where the yield response was affected by rainfall and other factors. The yield response lagged by one year, as LOM introduced at the start of the production season affected the yields later. Therefore, the LOM values were shifted forward by one year for better alignment (see Fig. 1).

 

Fig. 1. LOM was horizontally shifted by one year for better analysis, with yield plotted over the years 1993–2020. The broken line represents standardized yield, while the solid line represents LOM.

Рис. 1. Для более эффективного анализа значения УМ были смещены по горизонтали на один год, при этом использовались соответствующие данные по урожайности за 1993–2020 годы. Пунктирная линия обозначает стандартизированную урожайность, а сплошная линия — УМ.

 

Trend similarity and statistical analysis

The analysis aimed to determine whether the two datasets had similar trends. The slope (%) of the LOM and yield trendlines (Fig. 2) were 0.038 and 0.053, respectively (with a small slope difference of 0.015%). The interaction term’s p-value was 0.123, exceeding the critical p-value of 0.05, indicating no significant difference between the trends. Overall, the rising slope indicated that over the past 28 years, an increase in LOM has been associated with an increase in the yield.

 

Fig. 2. Trend Similarity between the LOM (red solid line) and crop yield (dark broken line) over the years 1993–2020.

Рис. 2. Сходство трендов УМ (красная сплошная линия) и урожайности сельскохозяйственных культур (тёмная пунктирная линия) за период 1993–2020 годов.

 

DTW similarity analysis

The initial segment of the optimal path (Fig. 4), from (1995, 1995) to (2001, 2001), shows a diagonal alignment between yield and LOM, indicating their close temporal proximity (Fig. 3), before diverging from (2002, 2001) to (2005, 2001). A deviation from the diagonal indicates compression and expansion of the time axis, as one element matches many (Fig. 3), reflecting the temporal variance between yield and LOM. The optimal cumulative cost path navigated the cost matrix by addressing the length differences. Finally, the path followed the matrix’s diagonal from (2017, 2016) to (2021, 2020), representing the temporal invariance between the datasets (see Fig. 4).

 

Fig. 3. DTW distance matching involves repeating or compressing points to minimize the distance between them.

Рис. 3. Сопоставление расстояний по методу ДТВ подразумевает повторение или сжатие точек для минимизации расстояния между ними.

 

Fig. 4. Optimal similarity path between the LOM and crop yield from 1993 to 2020.

Рис. 4. Оптимальный путь сходства УМ и урожайности сельскохозяйственных культур за период с 1993 по 2020 годы.

 

Evaluation of the DTW distance similarity performance

The DTW distance performance evaluation metrics were as follows: standard deviation (7.56 × 10⁻³), mean (1.08 × 10⁻²), minimum (1.42 × 10⁻⁵), and maximum (3.220 × 10⁻²). The MAE and RMSE were calculated as 6.33 × 10⁻³ and 7.56 × 10⁻³, respectively. Based on these evaluation metrics, further interpretation is provided in the discussion section.

Discussion

Overall, 44.4% of the elements in the two sequences showed perfect temporal matching, indicating that the timing of the yield and LOM was aligned (see Fig. 4) and, that the yield was responding to fluctuations in the LOM for 44.4% of the years. In the remaining years, other factors, such as rainfall, had a greater influence on the yield. However, there was some similarity in the other sections of the pair of sequences, possibly suppressed by additional factors. The similarity score was 34, indicating 34 pairs of aligned elements between the two sequences, which reflects a comparatively higher degree of similarity.

The level of similarity was assessed using average similarity, consistency, alignment quality, and error metrics. The mean DTW distances were relatively low, suggesting a fairly similar time series sequences, on average. The standard deviation of the DTW distances is relatively low, indicating consistent similarity across the dataset. The minimum DTW distance is small, indicating good alignment between sequences, although some instances show larger DTW distances, suggesting occasional poor alignment. The small MAE and RMSE values indicate close observed DTW distances.

Conclusion

The OLS regression and DTW analysis show a steady increase in LOM and crop yields in Eritrea over the past 28 years with no significant trend differences, despite low growth rates. Furthermore, the DTW analysis reveals that 44.4% of the yield variations correlate with fluctuations in the LOM. This implies that mechanizing agricultural operations in Eritrea significant impacts crop yield, highlighting the need for enhancing LOM in the country. The mean distances, standard deviation, minimum value, and error metrics show similar patterns in both datasets over the years. However, the analysis showed minor disparities in cereal yields with respect to LOM. While the LOM significantly enhances agricultural productivity, as seen in the upward trend and optimal alignment of the DTW method, variations in alignment in certain years suggest that other factors, such as climatic conditions, also significantly impact yield. To augment LOM’s role in crop yield, recommendations include aligning agricultural mechanization with sustainable practices, developing adaptable climate policies, investing in new technologies, and reinforcing environmentally friendly policies for mechanization for sustained development of Eritrea’s agricultural sector.

Additional information

Author contributions: T.A. Medhn: conceptualization, study design, data collection, methodology, formal analysis, writing — original draft; A.G. Levshin: technical advice and guidance throughout the research process; S.G. Teklay: writing — review and editing, enhancing clarity. Thereby, all authors made a substantial contribution to the conception of the work, acquisition, analysis, interpretation of data for the work, drafting and revising the work, final approval of the version to be published and agree to be accountable for all aspects of the work.

Ethics approval: Not applicable.

Funding sources: No funding.

Disclosure of interests: The authors have no relationships, activities or interests for the last three years related with for-profit or non-profit third parties whose interests may be affected by the content of the article.

Statement of originality: When creating this work, the authors did not use previously published information (text, illustrations, data).

Data availability statement: The editorial policy regarding data sharing is not applicable to this work, and no new data has been collected or created.

Generative AI: Generative AI technologies were not used for this article creation.

Provenance and peer-review: This work was submitted to the journal on its own initiative and reviewed according to the usual procedure. One external reviewer, a member of the editorial board and the scientific editor of the publication participated in the review.

About the authors

Tesfit A. Medhn

Mai-Nefhi College of Engineering and Technology; Russian State Agrarian University — Moscow Timiryazev Agricultural Academy; Addey Agricultural and Food Cooperative

Author for correspondence.
Email: noahtesas@gmail.com
ORCID iD: 0009-0002-4371-1323
SPIN-code: 9344-9472

postgraduate in the Operation of Machinery and Tractor Fleet Department

Eritrea, Asmara; Moscow, Russia; Budapest, Hungary

Alexander G. Levshin

Russian State Agrarian University — Moscow Timiryazev Agricultural Academy

Email: alevshin@rgau-msha.ru
ORCID iD: 0000-0001-8010-4448
SPIN-code: 1428-5710

Dr. Sc. (Engineering), Professor

Russian Federation, Moscow

Simon G. Teklay

Mai-Nefhi College of Engineering and Technology; New Mexico State University

Email: gtsimon1994@gmail.com
ORCID iD: 0009-0002-3336-0523

M. Sc., Graduate Research Assistant, Water Science and Management Program; Department of Animal and Range Sciences; College of Agriculture, Consumer and Environmental Sciences

Eritrea, Asmara; Las Cruces, USA

References

Supplementary files