1. THE COMPLETE TITLE OF ONE (OR MORE) PAPER(S) PUBLISHED IN THE OPEN LITERATURE DESCRIBING THE WORK THAT THE AUTHOR CLAIMS DESCRIBE A HUMAN-COMPETITIVE RESULT;
An evolutionary parsimonious approach to estimate daily reference evapotranspiration
https://doi.org/10.1038/s41598-024-56770-3

2. THE NAME, COMPLETE PHYSICAL MAILING ADDRESS, E-MAIL ADDRESS, AND PHONE NUMBER AND PHONE NUMBER OF EACH AUTHOR OF EACH PAPER(S);
Francisco Javier Ruiz Ortega
•	TecNM/CENIDET, Interior Internado Palmira S/N, Palmira, 62493 Cuernavaca, Mor.
•	TecNM/I.T. Torreón, Carretera Torreón- San Pedro De las Colonias KM 7.5, Ejido Ana, 27170 Torreón, Coah.
D20ce082@cenidet.tecnm.mx
ORCID 0000-0001-6174-6218
Teléfono: +52 (871) 1042066

Eddie Clemente
•	TecNM/I.T. Ensenada, Blvd. Tecnológico 150, Ex-ejido Chapultepec, Código Postal 22780, Ensenada, B.C., México
eclemente@ite.edu.mx 
ORCID 0000-0003-3195-9540
Teléfono: +52 (646) 1174821

Alicia Martínez Rebollar
•	TecNM/CENIDET, Interior Internado Palmira S/N, Palmira, 62493 Cuernavaca, Mor.
alicia.mr@cenidet.tecnm.mx 
ORCID 0000-0002-1071-8599
Teléfono: +52 (777) 2676080

José Jassón Flores Prieto
•	TecNM/CENIDET, Interior Internado Palmira S/N, Palmira, 62493 Cuernavaca, Mor.
jose.fp@cenidet.tecnm.mx 
ORCID 0000-0001-7408-6589
Teléfono: +52 (777) 2572622

3. CORRESPONDING AUTHOR (I.E., THE AUTHOR TO WHOM NOTICES WILL BE SENT CONCERNING THE COMPETITION) AUTOR CORRESPONDIENTE (ES DECIR, EL AUTOR A QUIEN SE ENVIARÁN LOS AVISOS REFERENTES A LA COMPETENCIA):
Francisco Javier Ruiz Ortega
D20ce082@cenidet.tecnm.mx

4. THE ABSTRACT OF THE PAPER(S);
The reference evapotranspiration (ETo) is an essential component in hydrological and ecological processes. The objective of this research is to develop an explicit model to estimate ETo only using commonly measurable meteorological parameters such as relative humidity, air temperature, and wind speed, where the measurements corresponding to solar radiation are omitted. The model was generated using Genetic Programming (GP), evaluated, and validated with reference data ETo using FAO56-PM. This reference data was obtained from different climates (warm-temperate and arid-warm) and latitudes, acquired from CIMIS stations in the state of California, United States, and the El Porvenir station in the state of Coahuila, located in north-central Mexico. After applying the proposed methodology, a total of 3754 results were generated, demonstrating a significant improvement in the estimation of ETo compared to the Hargreaves–Samani model. A particularly noteworthy result revealed that our approach outperformed the Hargreaves–Samani model in the training phase by 27%, and in the testing phase by 16%, on average. In order to achieve a generalized model, a dataset encompassing meteorological stations in two different climates (warm-temperate and arid-warm) and various latitudes was utilized. The obtained outcome unveiled a highly effective model for estimating ETo in diverse climatic contexts, eliminating the need for local adjustments. This model significantly surpassed the Hargreaves–Samani model, exhibiting superior performance by 17% during the training phase and 18% during the testing phase. These results conclusively underscore the capability of our approach to provide more accurate and reliable ETo estimates. Finally, to validate the model, four different datasets with climates similar to those used for model creation (warm-temperate, warm-arid) and different latitudes were employed. The validation stage results clearly indicate the superiority of our reference evapotranspiration ETo11 model over the Hargreaves–Samani model by 51% in warm-temperate climates. For the dataset with arid-warm climate, our model continued to show satisfactory results, surpassing the Hargreaves–Samani model by 8%. GP emerges as an innovative and effective alternative for simplified model development. This approach introduces a novel paradigm that facilitates the efficient development of models, standing out for its simplicity and effectiveness in generating solutions.

5. A LIST CONTAINING ONE OR MORE OF THE EIGHT LETTERS (A, B, C, D, E, F, G, OR H) THAT CORRESPOND TO THE CRITERIA (SEE ABOVE]) THAT THE AUTHOR CLAIMS THAT THE WORK SATISFIES;
(A) The result was patented as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention.
(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.
(C) The result is equal to or better than a result that was placed into a database or archive of results maintained by an internationally recognized panel of scientific experts.
(D) The result is publishable in its own right as a new scientific result independent of the fact that the result was mechanically created.
(G) The result solves a problem of indisputable difficulty in its field.

6. A STATEMENT STATING WHY THE RESULT SATISFIES THE CRITERIA THAT THE CONTESTANT CLAIMS (SEE EXAMPLES OF STATEMENTS OF HUMAN-COMPETITIVENESS AS A GUIDE TO AID IN CONSTRUCTING THIS PART OF THE SUBMISSION);
(A) The result was patented as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention.
Our models developed using this methodology can be integrated as key components in automated irrigation systems and measurement devices, which are patentable. Consequently, our methodology meets the requirements for patentability by representing an innovative method for estimating reference evapotranspiration. This approach is not only applicable in the design of measurement instruments but also contributes to characterizing the physical phenomenon involving the transfer of water from the Earth's surface to the atmosphere. Some examples of patents include:
WO1998054953A1. An Autonomous Ecological Irrigation System immune to blockages, capable of cost-effectively addressing conservationist and uniformly distributed irrigation of a variety of cultivated areas; automatically operating a succession of fertigation cycles, requiring minimal driving energy and a reduced flow of incoming water. The system allows for implementations of diverse configurations, comprising a plurality of local subsystems (1), controllable locally or from a remote station (6); each subsystem comprising: a container (2) capable of accumulating the volume of liquid to be discharged per cycle; an irrigation actuator set (3) capable of regulating the volume to be irrigated and discharging it upon receiving a low-energy signal; a low-consumption electronic control set (4) capable of determining the frequency and the appropriate time to send said signal; and a low-restriction distribution network (5), capable of transporting irrigation flow to the utilization locations.
ES2214966B2.- Autonomous equipment for water management and irrigation control, being the type of equipment used for controlling irrigation water consumption. It consists of a body (1), preferably made of stainless steel, defined by a water passage tube (2) and a tube (3) positioned perpendicular to tube (2), containing the functional elements. Regarding the water flow passage tube (2) (15), it has a single moving part (4). The autonomous equipment comprises functional elements defined by sensors (5) that detect the movement of a moving part (4), a microcontroller (6), a memory (7), a display (8), and a bidirectional communication interface (9). The autonomous equipment is powered by at least one battery (10), and it processes, stores, and transmits information independently.
ES2345581T3.- This invention relates to a method and an apparatus for measuring evaporation. In this method, the temperatures (t k, t m, t) are determined for a comparison piece (6) essentially in the non-evaporation state, for a comparison piece (8) essentially in the evaporation state, and for the measured object (1). Based on a comparison between the obtained temperature values (t k, t m, t), the evaporation index (n) is determined as a function of the amount of liquid evaporated.
(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.
The models generated through genetic programming (GP) are directly compared with the human-developed Hargreaves-Samani model (Hargreaves & Samani, 1985), which is widely recognized and endorsed by the Food and Agriculture Organization of the United Nations (FAO). In this context, the advancements achieved outperform this model, coming closer to the reference standard of Penman-Monteith (Allen, Pereira, Raes, & Smith, 1998).
(C) THE RESULT IS EQUAL TO OR BETTER THAN A RESULT THAT WAS PLACED INTO A DATABASE OR ARCHIVE OF RESULTS MAINTAINED BY AN INTERNATIONALLY RECOGNIZED PANEL OF SCIENTIFIC EXPERTS.
In May 1990, the FAO organized a consultation of experts and researchers, in collaboration with the International Commission on Irrigation and Drainage and the World Meteorological Organization, to review FAO methodologies for determining crop water requirements and to produce guidelines for the revision and updating of the procedures used. The panel of experts recommended the adoption of the Penman-Monteith combined method as the new standard procedure for reference evapotranspiration and outlined the procedures for calculating the various parameters included in the method. However, for locations where there are not enough parameters available to use the Penman-Monteith model, the FAO recommends the Hargreaves-Samani method. The results show that our approach outperformed the Hargreaves-Samani model by 27% during the training phase and by 16% during the testing phase.
(D) THE RESULT IS PUBLISHABLE IN ITS OWN RIGHT AS A NEW SCIENTIFIC RESULT  INDEPENDENT OF THE FACT THAT THE RESULT WAS MECHANICALLY CREATED.
The analysis of nonlinear models constructed using genetic programming (GP) demonstrates that they can accurately assess reference evapotranspiration across various climates or, alternatively, specialize a model for a particular geographic region. The proposed models involve only common and easily obtainable climatic variables, such as temperature, relative humidity, and wind speed.
This is relevant in areas such as agriculture, hydrology, water resource management, meteorology, climatology, ecology, environmental science, civil engineering, and soil science. It is crucial for irrigation management, hydrological modeling, climate regulation, ecosystem conservation, and infrastructure planning. Proper understanding and management of water are vital for sustainability, efficient use of natural resources, and environmental conservation, while also generating significant economic savings for governments and companies. Between 1980 and 2017, the cost of water in agricultural production was $1.11 per cubic meter (Montesillo-Cedillo, 2023). The social cost of water, which includes economic, environmental, and social impacts, is even higher. According to the "World Water Development Report 2024" by the UN, sustainable and equitable water management can promote peace and prosperity, while its scarcity or contamination can lead to food insecurity, loss of livelihoods, and conflicts (Abbara et al., 2024). A simple and effective model that uses easily measurable variables is a valuable contribution to the community.
(G) THE RESULT SOLVES A PROBLEM OF INDISPUTABLE DIFFICULTY IN ITS FIELD.
Despite the variety of methods available to estimate reference evapotranspiration, the search for more accurate and reliable alternatives continues due to the need to improve its accuracy in diverse climatic and geographical conditions, using the least number of meteorological parameters possible in a simple and practical manner. This challenge lies in the necessity for models to be robust and reliable, regardless of the geography, climate, and location of the study area, while also considering phenomena such as climate change and dynamic environmental conditions. Models must be simple and interpretable for real-world application to efficiently manage water resources, especially in areas with limitations in this resource.
These demands have driven the use of technological advancements to develop more effective methods applicable to different spatial and temporal scales. For example, satellite data, advanced numerical models, and machine learning techniques are used to achieve more precise and reliable estimates of evapotranspiration, whose accuracy is crucial for informed decision-making in water management and environmental planning. Therefore, our approach provides a method to construct nonlinear models that accurately, practically, and interpretable estimate reference evapotranspiration. Specifically, the proposed models have been numerically evaluated under diverse climatic conditions and latitudes, overcoming the common challenge of adjusting local or specific models for use in a particular region.

7. A FULL CITATION OF THE PAPER (THAT IS, AUTHOR NAMES; TITLE, PUBLICATION DATE; NAME OF JOURNAL, CONFERENCE, OR BOOK IN WHICH ARTICLE APPEARED; NAME OF EDITORS, IF APPLICABLE, OF THE JOURNAL OR EDITED BOOK; PUBLISHER NAME; PUBLISHER CITY; PAGE NUMBERS, IF APPLICABLE);
Ruiz-Ortega, F.J., Clemente, E., Martínez-Rebollar, A. et al. An evolutionary parsimonious approach to estimate daily reference evapotranspiration. Sci Rep 14, 6736 (2024). https://doi.org/10.1038/s41598-024-56770-3

8. A STATEMENT EITHER THAT "ANY PRIZE MONEY, IF ANY, IS TO BE DIVIDED EQUALLY AMONG THE CO-AUTHORS" OR A SPECIFIC PERCENTAGE BREAKDOWN AS TO HOW THE PRIZE MONEY, IF ANY, IS TO BE DIVIDED AMONG THE CO-AUTHORS;
Any cash prize, if available, will be distributed equitably among all co-authors involved in the work. This fair distribution recognizes and values each co-author's contribution to the research, thus fostering an environment of collaboration and mutual recognition within the team. This equitable approach not only promotes fairness and respect among collaborators but also encourages cooperation and shared commitment towards the joint success of the research.

9. A STATEMENT STATING WHY THE AUTHORS EXPECT THAT THEIR ENTRY WOULD BE THE "BEST," AND
The accurate estimation of reference evapotranspiration is crucial and brings about significant benefits for humanity, the environment, agricultural producers, and climate change management. Firstly, evapotranspiration is a vital component of the hydrological cycle, representing water loss from the soil due to direct evaporation and plant transpiration. An accurate estimation of this process is crucial for sustainable water management, allowing for proper allocation of water resources for both human use and natural ecosystems.
Evapotranspiration directly influences agricultural productivity and food security. Farmers require accurate estimations of evapotranspiration to efficiently plan their irrigation and improve water management in their crops. Proper management of this process helps increase irrigation efficiency, reduce water waste (where the loss of one millimeter of water per hectare is equivalent to 10,000 liters), and enhance crop quality. These aspects, in turn, have a positive impact on food production and agricultural economy. For example, in Mexico, the agricultural land covers a total of 106,891,000 ha, as detailed in the report by Gomez (Gómez, Cauich, Batista, & José, 2024). If we extrapolate that the loss of one millimeter of water per hectare is equivalent to 10,000 liters, globally, this would translate to 1,068,910,000 m-3 of water. Economically, this amount would represent a value of $1,186,490,100 (one billion one hundred eighty-six million four hundred ninety thousand one hundred pesos).
In environmental terms, accurate estimation of reference evapotranspiration is crucial for understanding and mitigating the effects of climate change. Changes in evapotranspiration patterns can affect water availability, vegetation distribution, and ecosystem response to extreme weather conditions. By improving the accuracy of evapotranspiration estimation, planning and adoption of adaptation and mitigation measures against the impacts of climate change are facilitated, promoting resilience of ecosystems and human communities.
In summary, accurately estimating reference evapotranspiration has a significant impact on sustainable water management, agricultural productivity, food security, environmental conservation, and climate change adaptation. It is a key component in decision-making related to the use and conservation of natural resources, and its importance extends to multiple aspects fundamental for human well-being and planetary health.
Considering the relevance of the addressed problem, we firmly believe that our work has several merits and contributions to the state of the art and the development of practical applications:

a)	We have proposed a novel method that applies GP for constructing nonlinear models as a solution to an environmental problem and water resource management. Our approach considers its application to agricultural production systems, which directly translates into benefits for food security and environmental conservation.
b)	The method has the potential to be patented as it addresses a complex problem covering various aspects: environmental, as it affects the water balance and ecosystem health; agricultural, as it influences irrigation management and crop productivity; economic, since water use efficiency is crucial for the financial viability of agriculture; water resource management, as it is essential for planning and equitable distribution of water among different users; and climate-related, as changes in evapotranspiration can alter water availability and exacerbate extreme events, impacting both communities and ecosystems.
c)	The design of the method with genetic programming (GP) is grounded in expert knowledge provided by the FAO56-PM method. This integration allows for more efficient and guided model search, evolving more effectively through generations. Thanks to this approach, the evolutionary algorithm can leverage the structure and critical variables identified by the FAO56-PM method, significantly reducing the number of executions required compared to other machine learning techniques. Consequently, the model not only achieves greater accuracy and robustness but also improves in terms of computational efficiency, making it a simple and interpretable solution for estimating reference evapotranspiration.
d)	Our article presents practical advantages over existing human solutions. The evolved nonlinear models are constructed using meteorological parameters such as air temperature, relative humidity, wind speed. This implies that these models can be used with measurements obtained from weather stations equipped with basic and low-cost instrumentation.
e)	Overall, the models evolved with GP to estimate reference evapotranspiration outperform the Hargreaves-Samani model, developed by humans, and represent a significant advancement in the scientific community.
f)	Accurate estimation of evapotranspiration is crucial for food security as it allows for efficient irrigation management, optimizing water resource use, and ensuring that crops receive the right amount of water at the right time. This not only improves the yield and quality of produced food but also increases agricultural productivity, essential to meet the growing demand for food. By promoting sustainable agricultural practices, accurate evapotranspiration estimation helps conserve water resources and makes agricultural systems more resilient to adverse climate conditions, such as droughts. Additionally, by avoiding excessive water and other input use, production costs are reduced, making agriculture more accessible and affordable for developing countries, small, and medium-scale producers. Together, these benefits significantly contribute to food security, ensuring more efficient, sustainable, and productive food production. 
For these reasons, we strongly believe that our model deserves to be selected as the winner of the contest due to its positive impact in various areas such as science, environmental conservation, and sustainable agriculture development.

10. AN INDICATION OF THE GENERAL TYPE OF GENETIC OR EVOLUTIONARY COMPUTATION USED, SUCH AS GA (GENETIC ALGORITHMS), GP (GENETIC PROGRAMMING), ES (EVOLUTION STRATEGIES), EP (EVOLUTIONARY PROGRAMMING), LCS (LEARNING CLASSIFIER SYSTEMS), GI (GENETIC IMPROVEMENT), GE (GRAMMATICAL EVOLUTION), GEP (GENE EXPRESSION PROGRAMMING), DE (DIFFERENTIAL EVOLUTION), ETC.
GP (Genetic Programming)

11. THE DATE OF PUBLICATION OF EACH PAPER.  IF THE DATE OF PUBLICATION IS NOT ON OR BEFORE THE DEADLINE FOR SUBMISSION, BUT INSTEAD, THE PAPER HAS BEEN UNCONDITIONALLY ACCEPTED FOR PUBLICATION AND IS “IN PRESS” BY THE DEADLINE FOR THIS COMPETITION, THE ENTRY MUST INCLUDE A COPY OF THE DOCUMENTATION ESTABLISHING THAT THE PAPER MEETS THE "IN PRESS" REQUIREMENT.
Date of publication: March 2024
Publication record https://doi.org/10.1038/s41598-024-56770-3
Received on November 11, 2023, March 11, 2024,
Available online on March 20, 2024.


References
Abbara, A., Shomar, R. A., Daoudy, M., Sittah, G. A., Zaman, M. H., & Zeitoun, M. J. T. L. (2024). Water, health, and peace: a call for interdisciplinary research. 403(10435), 1427-1429. 
Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. J. F., Rome. (1998). Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. 300(9), D05109. 
Gómez, C. S., Cauich, I. C., Batista, B. d. P., & José, C. C. L. J. R. d. l. U. d. Z. (2024). Análisis de la situación agrícola de la República Mexicana. 15(42), 8-36. 
Hargreaves, G. H., & Samani, Z. A. J. A. e. i. a. (1985). Reference crop evapotranspiration from temperature. 1(2), 96-99. 
Montesillo-Cedillo, J. L. J. R. m. d. c. a. (2023). Valor del agua en la producción agrícola bajo riego en México. 14(8).