Simple Kriging for Rainfall Mapping: A Geostatistical Analysis of North East Amhara (Wollo), Ethiopia Using ArcMap Pro.

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Moges Gtachew Ebrea, Netsanet Habtamu, Terefe Hundessa, This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6457750/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background: Accurate spatial estimation of rainfall is essential for informed agricultural planning, sustainable water resource use, and climate resilience, particularly in data-scarce regions like North East Amhara (Wollo), Ethiopia.. In North East Amhara (Wollo), Ethiopia, rainfall data is often sparse and unevenly distributed, making it necessary to evaluate the spatial pattern of available rainfall gauge data for accurate interpolation and analysis. Method: This study compiled rainfall data from 55 meteorological stations, incorporating geographic and climatic variables such as mean annual rainfall, elevation, latitude, and longitude. Missing data were addressed to ensure completeness. Spatial distribution was visualized using ArcMap Pro, and Exploratory Spatial Data Analysis (ESDA) was conducted through histogram and Normal QQ plot analysis. To generate continuous rainfall surfaces, three interpolation methods Simple Kriging, Ordinary Kriging, and Universal Kriging were applied and evaluated using cross-validation metrics. Result: Simple Kriging emerged as the most accurate interpolation method. The spatial analysis revealed heterogeneous rainfall distribution, with low rainfall in the eastern and northern zones, high rainfall in the southwest, and moderate rainfall in the north-central region. A classification system was applied to categorize rainfall into low, medium, and high ranges, aiding in regional planning. Conclusion: The findings offer critical insights into the spatial rainfall patterns of North East Amhara and support the development of adaptive strategies such as drought-resistant crops, water-saving techniques, water storage infrastructure, and early warning systems. Long-term rainfall analysis is recommended to strengthen future planning and climate resilience efforts. Climate Analysis and Modeling Geographic Information Systems Physical Geography Rainfall distribution Spatial analysis Kriging GIS Interpolation North East Amhara Climate planning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction In Ethiopia, where over 90% of agriculture is rain-fed, fluctuations in rainfall present a significant challenge to food security, water availability, and rural livelihoods. This is particularly pronounced in the North East Amhara region (Wollo), where topographic and climatic diversity amplify spatial rainfall disparities, particularly in regions with limited meteorological infrastructure (Dinku et al., 2021 ; Gebrehiwot et al., 2022 ; Abegaz et al., 2023 ). In Africa, where over 90% of agriculture is rain-fed, accurate rainfall estimation is essential for food security, drought mitigation, and sustainable land management (Teshome et al., 2023 ; Gebrehiwot et al., 2023 ; Abegaz et al., 2024 ). Ethiopia's diverse topography, spanning from arid lowlands to humid highlands, results in significant spatial and temporal rainfall variability, highlighting the need for accurate interpolation techniques for regional climate studies (Tsegaye et al., 2023 ; Melesse et al., 2023 ; Deressa et al., 2024 ). The northeastern Amhara region (Wollo), Ethiopia, is particularly vulnerable due to its complex climatic gradients, where rainfall distribution is heavily influenced by elevation, orographic effects, and seasonal monsoon dynamics (Teferi et al., 2013 ; Gebremicael et al., 2013 ). However, the region suffers from a sparse and unevenly distributed rain gauge network, leading to significant data gaps that hinder accurate hydrological modeling and climate adaptation planning (WMO, 2018; Li & Heap, 2014 ). In many developing countries, meteorological stations are often clustered in accessible areas, leaving remote and topographically complex regions underrepresented (Dinku et al., 2021 ; Gebrehiwot et al., 2022 ; Abegaz et al., 2023 ). Ethiopia exemplifies this challenge, where highland areas receive substantial rainfall while lowland regions experience prolonged droughts, yet monitoring infrastructure remains inadequate" (Fenta et al., 2023 ; Tesfaye et al., 2023 ; Tadesse et al., 2024 ). The scarcity of ground-based rainfall data necessitates the use of spatial interpolation techniques to estimate precipitation in ungauged locations (Hu et al., 2023 ). Traditional methods such as Thiessen polygons and Inverse Distance Weighting (IDW) provide simplistic estimations but fail to account for spatial autocorrelation and elevation-induced rainfall variability (Arianti et al., 2018 ). Geostatistical approaches, particularly Kriging, have emerged as superior alternatives due to their ability to incorporate spatial dependence and uncertainty quantification (Li & Heap, 2014 ). Kriging, a family of geostatistical interpolation methods, has gained prominence in climatology and hydrology for its robustness in handling spatially correlated data (Coburn, 2000 ). Unlike deterministic methods, Kriging employs variogram models to characterize spatial relationships, enabling optimal predictions at unsampled locations while providing error estimates (Belkhiri et al., 2021 ). The three primary Kriging variants simple, ordinary, and universal differ in their assumptions about stationarity and trend components, with each offering distinct advantages based on the characteristics of the data (McLennan et al., 2006 ). Simple Kriging assumes a known mean, Ordinary Kriging estimates it locally, and Universal Kriging incorporates external drift variables such as elevation (Li & Heap, 2014 ). Recent studies have demonstrated that Universal Kriging outperforms other methods in mountainous regions where rainfall is strongly elevation-dependent (Caballero et al., 2013 ).​ The integration of Geographic Information Systems (GIS) and remote sensing has significantly enhanced Kriging applications by providing high-resolution elevation data (e.g., LiDAR, Sentinel-2) and auxiliary variables (e.g., NDVI, slope) for improved spatial interpolation (Li et al., 2024 ). Recent advancements combine Kriging with machine learning (e.g., Random Forests) to optimize predictions in hydrology and precision agriculture (Wang et al., 2023 ). Additionally, UAV-based remote sensing now enables real-time Kriging interpolation for dynamic environmental monitoring (García et al., 2024 ). ArcMap Pro, with its Geostatistical Analyst tools, enables comprehensive exploratory spatial data analysis (ESDA), variogram modeling, and cross-validation, ensuring optimal model selection (Ghahraman et al., 2021 ). Cross-validation techniques, including root mean square error (RMSE) and mean absolute error (MAE), are critical for assessing interpolation accuracy and identifying potential biases (Blanchet et al., 2023 ). Despite these advancements, few studies have systematically compared Kriging variants in Ethiopia’s northeastern highlands, leaving a gap in localized rainfall interpolation methodologies (Mekonen & Berlie, 2019 ). The northeastern Amhara region (Wollo) is a climatic transition zone where rainfall patterns vary drastically between highland plateaus and lowland valleys (Mekonen & Berlie, 2019 ; Tesfaye et al., 2020 ).This area affected by floods and droughts, and thus precise estimation of rainfall is necessary for agricultural planning as well as minimizing disaster risks (Weldegerima & Gebresilassie, 2025 ; Mekonnen et al., 2025 ). Past studies in Ethiopia have primarily focused on the Blue Nile Basin or the central highlands, with little consideration given to Wollo's unique rainfall dynamics (Mekonen & Berlie, 2019 ; Tesfaye et al., 2020 ). Besides, although some research has applied Kriging in Ethiopian rainfall research, most of them applied Ordinary Kriging without evaluating the potential benefit of Universal Kriging with elevation covariates (Belkhiri et al., 2021 ; Shitu et al., 2023 ).This study addresses these gaps by To assess spatial distribution and rainfall gauge data quality in North East Amhara (Wollo), Ethiopia To compare three interpolation methods Simple, Ordinary and Universal Kriging for Interpolation of the rainfall using the ArcMap Pro. To give an accurate Rainfall distribution mapping to support the climate planning for agriculture and for water resource. Materials and methods Description of the study area The northeastern Amhara region is located in Ethiopia , roughly between 10°15' and 13°15' N latitude and 38°25' and 40°15' E longitude. This area covers parts of North East Amhara (Wollo), North Wollo, Waghemra, and Oromia Zone, positioned to the northeast of the country's central plateau. The climate in this region is diverse due to its varied topography. It includes Temperate (Dega) Found in the higher altitudes, characterized by cooler temperatures and higher rainfall,Subtropical (Woina Dega) Present in the mid-altitudes, with moderate temperatures and rainfall, Tropical (Kolla) Located in the lower altitudes, where temperatures are higher and rainfall is less frequent.Rainfall generally occurs during the main rainy season (June to September), with variability depending on altitude and local geographical features. The northeastern Amhara region is predominantly mountainous, featuring,Highlands and Plateaus these include some of Ethiopia's highest elevations, with significant peaks such as Mount Abuna Yosef in North Wollo, Deep Valleys and Gorges these are carved by rivers such as the Bashilo, contributing to the rugged terrain.Rolling Hills and Lowlands found in the lower altitudes, particularly in parts of Waghemra and Oromia Zone. The elevation in the region ranges from about 1,500 meters to over 4,000 meters above sea level, contributing to its climatic and ecological diversity. The objective of this project is to create a comprehensive spatial interpolation of rainfall patterns in North East Amhara (Wollo), Ethiopia, using Kriging techniques within ArcMap Pro. This section outlines the methods and steps involved in achieving this goal. Table 1 Data Type and Source Data Type Source Purpose Pre-processing Steps Rainfall Data Ethiopian Meteorological Agency Rainfall analysis and Kriging interpolation Check for missing values, outliers, inconsistencies; clean and correct Rain Gauge Station Data Field records, NEMA, of Ethiopia Spatial location of rain measurement points Coordinate verification, format harmonization DEM (Digital Elevation Model) Government portals, USGS Earth Explorer, SRTM Elevation-related spatial analysis Project to same CRS, clip to study area Ethiopia Shapefile Map GADM, DIVA-GIS, Administrative boundaries for mapping Reproject, clip, and align with DEM and rainfall layers Exploratory Data Analysis (EDA) In this stage, descriptive statistics were performed on the rainfall data to understand its basic characteristics, including measures such as the mean, standard deviation, and range (Papacharalampous et al., 2020 ). Visualizations, such as point maps, will be created to show the spatial distribution of rain gauge stations and identify any potential trends or patterns in the data (GhoshDastider et al., 2024 ). Spatial autocorrelation analysis of the rainfall data will also be conducted using variograms. Variograms illustrate the spatial dependence of data points based on their separation distance, helping to determine the most appropriate Kriging model for the interpolation (Kilibarda et al., 2020 ; Ly et al., 2021 ). Kriging Model Selection and Implementation Based on the variogram analysis, the appropriate Kriging model was selected. Ordinary Kriging, which assumes stationarity (constant mean) in the data, or Universal Kriging, which can account for spatial trends, may be used depending on the data characteristics (Ly et al., 2021 ; Kilibarda et al., 2020 ). ArcMap Pro's Geostatistical Analyst tools will be utilized to perform the Kriging interpolation. This process involves defining the Kriging model parameters based on the variogram analysis and the spatial coordinates of the rain gauge stations (Esri, 2023 ). Model Validation and Accuracy Assessment The performance of the selected Kriging model was evaluated using cross-validation techniques. This involves splitting the data into training and validation sets. The Kriging model was built using the training data, and then it was applied to predict rainfall values at the validation locations. The predicted values will be compared to the actual observed values to assess the model's accuracy. Statistical measures, such as Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), will be used to quantify the prediction errors and assess model performance (Ly et al., 2021 ; Kilibarda et al., 2020 ; Li & Heap, 2014 ). The following formulas are commonly used to evaluate the performance of geostatistical interpolation models, including Kriging. These metrics help quantify the prediction accuracy by comparing predicted rainfall values with actual observed data during cross-validation (Li & Heap, 2014 ; Ly et al., 2021 ). Root Mean Squared Error (RMSE) RMSE measures the square root of the average squared differences between predicted and observed values: ( 1 ) Where: • P i = predicted value at location i • O i = observed value at location i • n = total number of validation points Mean Absolute Error (MAE) MAE measures the average of the absolute differences between predicted and observed values: ( 2 ) Where: • P i = predicted value at location i • O i = observed value at location i • n = total number of validation points Once the Kriging interpolation is complete, the results was analyzed, and maps depicting the spatial distribution of interpolated rainfall across North East Amhara (Wollo) was generated. High-resolution, visually appealing maps were created using ArcMap Pro's cartographic tools. Relevant base layers, such as topography, and informative legends will be included to enhance the map's interpretability and provide context for the rainfall patterns. Software ArcMap Pro is the primary software used throughout this project. It employed for data analysis, performing the Kriging interpolation, and generating the spatial interpolation maps. Results and discussion Evaluating the Spatial Distribution of Rainfall Gauge Data in North East Amhara (Wollo), Ethiopia Assessing the spatial distribution of rainfall gauge data in North East Amhara (Wollo), Ethiopia. The analysis aims to prepare the data for interpolation by examining the completeness and spatial arrangement of the rainfall measurements. This process involves several steps, including data collection, spatial plotting, and exploratory spatial data analysis (ESDA). Collection and Rearrangement of Rainfall Data Rainfall data is collected from Ethiopian meteorological agencies, covering 55 stationsin the North East Amhara region. Key station details, including town name, wereda, region, zone, mean annual rainfall (RAIN), elevation, latitude (lat), and longitude (log), are recorded. Missing data is identified and addressed using techniques such as data imputation or excluding incomplete records to ensure dataset completeness for further analysis. Exploratory Spatial Data Analysis (ESDA) Exploratory Spatial Data Analysis (ESDA) is crucial for understanding the spatial characteristics of data prior to interpolation. In this study, ESDA was conducted to inform the selection of appropriate Kriging models for rainfall data in the North East Amhara region, Ethiopia. Histogram and Q-Q Plot Analysis Exploratory analysis of the rainfall data using a histogram revealed a right-skewed distribution, with a mean of 1,042.54 units and a median of 965.56 units. The skewness indicates a tendency toward higher rainfall values, while the kurtosis value of 2.7 suggests a distribution moderately close to normal. To further assess normality, a Q-Q plot was employed. The plot showed that the central values closely followed a normal distribution, whereas deviations at the tails indicated mild skewness or potential outliers. These findings underscore the importance of data transformation and normalization prior to geostatistical modeling. Data Transformation for Normality The skewness and kurtosis of the rainfall data were assessed before and after applying a log transformation. The transformation improved the data distribution, bringing it closer to normality. These preprocessing steps are crucial for enhancing the reliability of geostatistical interpolation methods such as Kriging (Li et al., 2022 ; Zhang et al., 2021; Ahmed et al., 2023 ). Kriging Interpolation Model Selection and Implementation To estimate the spatial distribution of rainfall in North East Amhara (Wollo), three Kriging techniques Simple Kriging, Ordinary Kriging, and Universal Kriging were applied using ArcMap Pro’s Geostatistical Analyst tools. Each model was selected based on underlying assumptions about the mean and spatial variability of the data. Review Cross-Validation Results Cross-validation results were assessed using key statistical metrics to evaluate model performance. The Mean Error indicates bias, where values closer to zero reflect minimal bias (Li & Heap, 2014 ; Ly et al., 2021 ). The Root Mean Square Error (RMSE) measures overall prediction accuracy, with lower values indicating better performance (Li & Heap, 2014 ; Blanchet et al., 2023 ). The Mean Standardized Error (MSE) like the mean error, should also be near zero for reliable predictions (Ly et al., 2021 ; Kilibarda et al., 2020 ). Lastly, the Root Mean Square Standardized Error (RMSSE) is ideally close to one, suggesting an appropriately modeled spatial structure. Table: 2 Cross-Validation Statistics of Kriging Models in ArcMap Pro Interpolation Method Count Mean Error RMSE MSE RMSSE Avg. Std. Error Simple Kriging 55 -4.51 83.97 -0.07 1.33 61.21 Ordinary Kriging 55 5.79 101.24 0.06 1.74 76.68 Universal Kriging 55 -6.88 106.58 0.08 1.74 369.5 Based on the cross-validation metrics, Simple Kriging emerged as the most effective interpolation method among the three models tested. It demonstrated the lowest Root Mean Square Error (83.974) and Average Standard Error (61.210), indicating high predictive accuracy. Additionally, it showed a Mean Error of -4.508 and a Mean Standardized Error of -0.073, both values being closest to zero, suggesting minimal bias. The Root Mean Square Standardized Error (1.334) was also nearest to the ideal value of 1. These combined results clearly indicate that Simple Kriging offers superior performance for spatial interpolation of rainfall in the study area. Accessing Standard Error Information in Kriging with ArcGIS Pro The kriging error map provides a visual representation of the spatial distribution of prediction errors across a region. The map identifies areas where kriging interpolation is more reliable (lighter shades) and where it is less reliable (darker shades). Addressing the high-error zones through additional data collection and refining the kriging model can enhance the overall accuracy and reliability of spatial predictions in this region. Rainfall distribution maps in North East Amhara (Wollo), Ethiopia Spatial analysis of rainfall patterns is vital for understanding climatic impacts on agriculture and water resources. In North East Amhara, Wollo, Ethiopia, this analysis highlights areas of varying rainfall, aiding effective resource management and planning (Gebremichael et al., 2014). Figure 9 presents the spatial distribution of interpolated rainfall data, crucial for assessing rainfall variability and supporting sustainable development strategies . The map illustrates a complex pattern of rainfall distribution across northeastern Amhara (Wollo).Low Rainfall Zones The eastern portionof the study area (Oromia Zone,) and eastern Wollo around Kalu displays the lowest rainfall amounts. Northwestern Lows The Waghemra Zone in the northern part of the study area also exhibits a low rainfall pattern. Similar to the eastern zone. Southwestern Highs In contrast, the southwestern part of the map, potentially within the South Wollo Zone, shows the highest rainfall. This area likely receives over 1,831 mm annually. North Wollo Moderation The north-central part of the map, likely representing North Wollo Zone, displays a moderate rainfall pattern. Rainfall distribution of the study area using Natural break classification scheme The "Natural Breaks (Jenks)" Reclassify tool in ArcGIS utilizes the Jenks Natural Breaks classification method to classify data into meaningful intervals. Developed by Jenks in the 1960s, this approach minimizes within-class variance while maximizing between-class variance to identify distinct groupings. ArcGIS automatically calculates breakpoints based on user-defined classes, facilitating the creation of thematic maps that effectively communicate spatial patterns. This tool is widely used in GIS applications for spatial analysis and visualization (Jenks, 1967 ; ESRI, n.d.; Steiniger & Hunter, 2013 ). Table 3 :Distribution of Rainfall class No Rainfall class Area/km2 Percentage 1 Low 29053.8 51.9 2 Medium 18915.3 33.7 3 High 8009.1 14.3 4 Total 55978.2 100 The table illustrates the distribution of rainfall classes within a specific area, based on Natural break class In the "Low Rainfall Class," an expanse of 29,053.8 km2 is accounted for, constituting approximately 51.90% of the total area.The "Medium Rainfall Class" encompasses an area of 18,915.3 km2, representing around 33.79% of the total area.Covering 8,009.1 km2, the "High Rainfall Class" comprises approximately 14.31% of the total area.The total area under consideration sums up to 55,978.2 km2, with each rainfall class contributing distinct proportions to the overall landscape. Conclusions This study examined rainfall gauge data in North East Amhara (Wollo), Ethiopia, to understand its spatial distribution. The goal was to prepare the data for interpolation, a technique used to estimate rainfall values in areas lacking rain gauges. The project involved collecting data from 55 stations across the region. Details like station name, location, elevation, and annual rainfall were recorded. Missing data was addressed to ensure the data set's completeness. Next, spatial analysis was conducted using ArcMap Pro. This included adding geographical coordinates to the data and visualizing rainfall patterns on a map with elevation shading. This visualization provided a clearer picture of rainfall distribution in relation to the region's topography. Exploratory Spatial Data Analysis (ESDA) was performed to gain insights into the data's characteristics. Histograms and QQ plots were used to assess the distribution of rainfall values. This analysis revealed a slight skew towards higher rainfall values, indicating that some areas receive significantly more rain than others. Several interpolation techniques, including Simple Kriging, Ordinary Kriging, and Universal Kriging, were considered. Based on cross-validation metrics, Simple Kriging proved to be the most suitable method for this data set. The final analysis focused on the spatial distribution of rainfall across the study area. The results depicted a complex pattern. The eastern portion and eastern Wollo around Kalu displayed the lowest rainfall. The Waghemra Zone in the north also exhibited low rainfall. In contrast, the southwestern part, likely representing South Wollo Zone, received the highest rainfall, exceeding. The north-central part experienced moderate rainfall. A classification scheme was employed to categorize the spatial distribution of rainfall into low, medium, and high classes. The analysis revealed that the low rainfall class covered the majority of the area (over 50%), followed by the medium rainfall class (around 33%), and lastly, the high rainfall class (approximately 14%).This study provides valuable information about the spatial patterns of rainfall in northeastern Amhara (Wollo). This knowledge can be used for various purposes, such as planning References Abegaz, A., Mekonnen, B., & Tadesse, Y. (2023). Spatiotemporal analysis of rainfall variability and trends in Ethiopia . Journal of Hydrology: Regional Studies, 45, 101262. https://doi.org/10.1016/j.ejrh.2023.101262 Abegaz, A., Teshome, G., & Fenta, A. A. (2024). Rainfall interpolation and trend analysis in the Ethiopian highlands. Climate Risk Management, 39, 100502. https://doi.org/10.1016/j.crm.2024.100502 Ahmed, A. A., Yilma, M., & Teshome, G. (2023). Improving rainfall interpolation using transformation techniques in data-scarce regions. 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(2020). Trends in rainfall and temperature extremes in Ethiopia. Climate, 8(1), 1–17. https://doi.org/10.3390/cli8010005 Tesfaye, A., Abegaz, A., & Tadesse, M. (2023). Monitoring drought events in Ethiopia using satellite data. Remote Sensing Applications: Society and Environment, 29, 100914. https://doi.org/10.1016/j.rsase.2022.100914 Teshome, G., Mekonnen, A., & Abegaz, A. (2023). Spatiotemporal rainfall mapping for agriculture in Ethiopia. Agricultural Water Management, 286, 108276. https://doi.org/10.1016/j.agwat.2023.108276 Tsegaye, T., Haileslassie, A., & Abegaz, A. (2023). Climate variability and agricultural resilience in the Ethiopian Highlands. Climate Services, 30, 100367. https://doi.org/10.1016/j.cliser.2023.100367 Wang, Y., Zhang, L., & Li, J. (2023). Kriging and machine learning for rainfall interpolation. Computers and Geosciences, 172, 105269. https://doi.org/10.1016/j.cageo.2023.105269 Weldegerima, T. M., & Gebresilassie, Y. T. (2025). Hydro-climatic hazards and adaptation strategies in Ethiopia. Environmental Research Letters, 20, 034012. https://doi.org/10.1088/1748-9326/acfc2f World Meteorological Organization (WMO). (2018). Guide to hydrological practices. Geneva: WMO-No. 168. https://library.wmo.int/ Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6457750","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":443471717,"identity":"b9cad63e-e9e6-432a-9aff-6981cf1a97ad","order_by":0,"name":"Moges Gtachew Ebrea","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEklEQVRIiWNgGAWjYHADHiCuqJEDMQ88IEK9BETLmWPGYC0JRGthbGFObABx8WnRbW+/+PDHL5s6/vazBx/zNrClzw87/BBoi52cbgN2LWZnzhQb8/alSUicyUs25t0hk7vxdpoBUEuysdkBHFpu5KRJM/YclmC4wWMmnXuGLXfj7ASQlgOJ23BrSf/5s+e/hPwNHvPfuW3M6Yaz0z8Q0JJ+jIHnxwEJA6AtzEAtCfLSOQRsOXOGWZq3IVly45kcY+k/Z44ZbpDOKTiQYIDHL8fbH3788ceOX+74GcOPMypq5OVnp2/+8KHCTg6XFmB0GDAwtiHxDcAqDXApBwH2BwwMf5D48g34VI+CUTAKRsFIBAAFrWgIQ1ATzQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0006-7642-9358","institution":"OdaBultum University","correspondingAuthor":true,"prefix":"","firstName":"Moges","middleName":"Gtachew","lastName":"Ebrea","suffix":""},{"id":443471718,"identity":"4d0361ed-0284-441f-8689-1fd57bf37310","order_by":1,"name":"Netsanet Habtamu","email":"","orcid":"","institution":"Addis Ababa University","correspondingAuthor":false,"prefix":"","firstName":"Netsanet","middleName":"","lastName":"Habtamu","suffix":""},{"id":443471719,"identity":"d85f0412-bc7c-4f80-a2f3-372f2aa7d059","order_by":2,"name":"Terefe Hundessa,","email":"","orcid":"","institution":"Addis Ababa University","correspondingAuthor":false,"prefix":"","firstName":"","middleName":"Terefe","lastName":"Hundessa","suffix":""}],"badges":[],"createdAt":"2025-04-15 20:18:36","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6457750/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6457750/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80788207,"identity":"f71b2033-dd76-4a9e-bf42-c4675786817f","added_by":"auto","created_at":"2025-04-17 06:21:54","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":225099,"visible":true,"origin":"","legend":"\u003cp\u003eStudy Area Map\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6457750/v1/6203c916b356f38f9a50c3fe.png"},{"id":80788205,"identity":"5822859f-3149-42cf-abe1-d76b6d94b178","added_by":"auto","created_at":"2025-04-17 06:21:54","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":126506,"visible":true,"origin":"","legend":"\u003cp\u003eMethodological flow chart\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6457750/v1/84af35c639e57d8a7da5b58c.png"},{"id":80788937,"identity":"a6cb333a-b0cd-4ebf-9f8e-2c647c772eeb","added_by":"auto","created_at":"2025-04-17 06:29:54","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":95768,"visible":true,"origin":"","legend":"\u003cp\u003eHistogram of Rainfall Data Distribution\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6457750/v1/64b958e1268f7c79c89e9a3e.png"},{"id":80788938,"identity":"98a980f0-eb43-4073-ae6a-2e73a89a943e","added_by":"auto","created_at":"2025-04-17 06:29:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":81069,"visible":true,"origin":"","legend":"\u003cp\u003eNormal Q-Q Plot of Rainfall Data\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6457750/v1/c31d0c9379b1c9440cff44bb.png"},{"id":80788214,"identity":"16c47f22-03db-4875-8e2c-1aa8e5d24a56","added_by":"auto","created_at":"2025-04-17 06:21:54","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":143832,"visible":true,"origin":"","legend":"\u003cp\u003eStandard Error map of the study area\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-6457750/v1/510e32e1a809336af7b065a1.png"},{"id":80788941,"identity":"d3e8808f-11ba-4228-bf7e-ca15a083069b","added_by":"auto","created_at":"2025-04-17 06:29:54","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":164645,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial Distribution of Rainfall\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-6457750/v1/bbe202c381d1035afe3b2d51.png"},{"id":80791095,"identity":"e33ea30e-cfde-40d6-b0c0-10b28253663d","added_by":"auto","created_at":"2025-04-17 06:45:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1534198,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6457750/v1/ac089ac3-c682-4369-834e-962f2c938f45.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eSimple Kriging for Rainfall Mapping: A Geostatistical Analysis of North East Amhara (Wollo), Ethiopia Using ArcMap Pro.\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn Ethiopia, where over 90% of agriculture is rain-fed, fluctuations in rainfall present a significant challenge to food security, water availability, and rural livelihoods. This is particularly pronounced in the North East Amhara region (Wollo), where topographic and climatic diversity amplify spatial rainfall disparities, particularly in regions with limited meteorological infrastructure (Dinku et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Gebrehiwot et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Abegaz et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In Africa, where over 90% of agriculture is rain-fed, accurate rainfall estimation is essential for food security, drought mitigation, and sustainable land management (Teshome et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Gebrehiwot et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Abegaz et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Ethiopia's diverse topography, spanning from arid lowlands to humid highlands, results in significant spatial and temporal rainfall variability, highlighting the need for accurate interpolation techniques for regional climate studies (Tsegaye et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Melesse et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Deressa et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The northeastern Amhara region (Wollo), Ethiopia, is particularly vulnerable due to its complex climatic gradients, where rainfall distribution is heavily influenced by elevation, orographic effects, and seasonal monsoon dynamics (Teferi et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Gebremicael et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). However, the region suffers from a sparse and unevenly distributed rain gauge network, leading to significant data gaps that hinder accurate hydrological modeling and climate adaptation planning (WMO, 2018; Li \u0026amp; Heap, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn many developing countries, meteorological stations are often clustered in accessible areas, leaving remote and topographically complex regions underrepresented (Dinku et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Gebrehiwot et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Abegaz et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Ethiopia exemplifies this challenge, where highland areas receive substantial rainfall while lowland regions experience prolonged droughts, yet monitoring infrastructure remains inadequate\" (Fenta et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Tesfaye et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Tadesse et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The scarcity of ground-based rainfall data necessitates the use of spatial interpolation techniques to estimate precipitation in ungauged locations (Hu et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Traditional methods such as Thiessen polygons and Inverse Distance Weighting (IDW) provide simplistic estimations but fail to account for spatial autocorrelation and elevation-induced rainfall variability (Arianti et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Geostatistical approaches, particularly Kriging, have emerged as superior alternatives due to their ability to incorporate spatial dependence and uncertainty quantification (Li \u0026amp; Heap, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eKriging, a family of geostatistical interpolation methods, has gained prominence in climatology and hydrology for its robustness in handling spatially correlated data (Coburn, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). Unlike deterministic methods, Kriging employs variogram models to characterize spatial relationships, enabling optimal predictions at unsampled locations while providing error estimates (Belkhiri et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe three primary Kriging variants simple, ordinary, and universal differ in their assumptions about stationarity and trend components, with each offering distinct advantages based on the characteristics of the data (McLennan et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Simple Kriging assumes a known mean, Ordinary Kriging estimates it locally, and Universal Kriging incorporates external drift variables such as elevation (Li \u0026amp; Heap, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Recent studies have demonstrated that Universal Kriging outperforms other methods in mountainous regions where rainfall is strongly elevation-dependent (Caballero et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).​\u003c/p\u003e \u003cp\u003eThe integration of Geographic Information Systems (GIS) and remote sensing has significantly enhanced Kriging applications by providing high-resolution elevation data (e.g., LiDAR, Sentinel-2) and auxiliary variables (e.g., NDVI, slope) for improved spatial interpolation (Li et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Recent advancements combine Kriging with machine learning (e.g., Random Forests) to optimize predictions in hydrology and precision agriculture (Wang et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Additionally, UAV-based remote sensing now enables real-time Kriging interpolation for dynamic environmental monitoring (García et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). ArcMap Pro, with its Geostatistical Analyst tools, enables comprehensive exploratory spatial data analysis (ESDA), variogram modeling, and cross-validation, ensuring optimal model selection (Ghahraman et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Cross-validation techniques, including root mean square error (RMSE) and mean absolute error (MAE), are critical for assessing interpolation accuracy and identifying potential biases (Blanchet et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Despite these advancements, few studies have systematically compared Kriging variants in Ethiopia’s northeastern highlands, leaving a gap in localized rainfall interpolation methodologies (Mekonen \u0026amp; Berlie, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe northeastern Amhara region (Wollo) is a climatic transition zone where rainfall patterns vary drastically between highland plateaus and lowland valleys (Mekonen \u0026amp; Berlie, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Tesfaye et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).This area affected by floods and droughts, and thus precise estimation of rainfall is necessary for agricultural planning as well as minimizing disaster risks (Weldegerima \u0026amp; Gebresilassie, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Mekonnen et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Past studies in Ethiopia have primarily focused on the Blue Nile Basin or the central highlands, with little consideration given to Wollo's unique rainfall dynamics (Mekonen \u0026amp; Berlie, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Tesfaye et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Besides, although some research has applied Kriging in Ethiopian rainfall research, most of them applied Ordinary Kriging without evaluating the potential benefit of Universal Kriging with elevation covariates (Belkhiri et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Shitu et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).This study addresses these gaps by\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cp\u003eTo assess spatial distribution and rainfall gauge data quality in North East Amhara (Wollo), Ethiopia\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo compare three interpolation methods Simple, Ordinary and Universal Kriging for Interpolation of the rainfall using the ArcMap Pro.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo give an accurate Rainfall distribution mapping to support the climate planning for agriculture and for water resource.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e "},{"header":"Materials and methods","content":"\u003cp\u003e\u003cstrong\u003eDescription of the study area\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe northeastern Amhara region is located in \u003cem\u003eEthiopia\u003c/em\u003e, roughly between 10\u0026deg;15\u0026apos; and 13\u0026deg;15\u0026apos; N latitude and 38\u0026deg;25\u0026apos; and 40\u0026deg;15\u0026apos; E longitude. This area covers parts of North East Amhara (Wollo), North Wollo, Waghemra, and Oromia Zone, positioned to the northeast of the country\u0026apos;s central plateau.\u003c/p\u003e\n\u003cp\u003eThe climate in this region is diverse due to its varied topography. It includes Temperate (Dega) Found in the higher altitudes, characterized by cooler temperatures and higher rainfall,Subtropical (Woina Dega) Present in the mid-altitudes, with moderate temperatures and rainfall, Tropical (Kolla) Located in the lower altitudes, where temperatures are higher and rainfall is less frequent.Rainfall generally occurs during the main rainy season (June to September), with variability depending on altitude and local geographical features.\u003c/p\u003e\n\u003cp\u003eThe northeastern Amhara region is predominantly mountainous, featuring,Highlands and Plateaus these include some of Ethiopia\u0026apos;s highest elevations, with significant peaks such as Mount Abuna Yosef in North Wollo, Deep Valleys and Gorges these are carved by rivers such as the Bashilo, contributing to the rugged terrain.Rolling Hills and Lowlands found in the lower altitudes, particularly in parts of Waghemra and Oromia Zone. The elevation in the region ranges from about 1,500 meters to over 4,000 meters above sea level, contributing to its climatic and ecological diversity.\u003c/p\u003e\n\u003cp\u003eThe objective of this project is to create a comprehensive spatial interpolation of rainfall patterns in North East Amhara (Wollo), Ethiopia, using Kriging techniques within ArcMap Pro. This section outlines the methods and steps involved in achieving this goal.\u003c/p\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 1\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eData Type and Source\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eData Type\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSource\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePurpose\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePre-processing Steps\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRainfall Data\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEthiopian Meteorological Agency\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRainfall analysis and Kriging interpolation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCheck for missing values, outliers, inconsistencies; clean and correct\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRain Gauge Station Data\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eField records, NEMA, of Ethiopia\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSpatial location of rain measurement points\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCoordinate verification, format harmonization\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDEM (Digital Elevation Model)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGovernment portals, USGS Earth Explorer, SRTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElevation-related spatial analysis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eProject to same CRS, clip to study area\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEthiopia Shapefile Map\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGADM, DIVA-GIS,\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAdministrative boundaries for mapping\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eReproject, clip, and align with DEM and rainfall layers\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eExploratory Data Analysis (EDA)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn this stage, descriptive statistics were performed on the rainfall data to understand its basic characteristics, including measures such as the mean, standard deviation, and range (Papacharalampous et al., \u003cspan\u003e2020\u003c/span\u003e). Visualizations, such as point maps, will be created to show the spatial distribution of rain gauge stations and identify any potential trends or patterns in the data (GhoshDastider et al., \u003cspan\u003e2024\u003c/span\u003e). Spatial autocorrelation analysis of the rainfall data will also be conducted using variograms. Variograms illustrate the spatial dependence of data points based on their separation distance, helping to determine the most appropriate Kriging model for the interpolation (Kilibarda et al., \u003cspan\u003e2020\u003c/span\u003e; Ly et al., \u003cspan\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eKriging Model Selection and Implementation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBased on the variogram analysis, the appropriate Kriging model was selected. Ordinary Kriging, which assumes stationarity (constant mean) in the data, or Universal Kriging, which can account for spatial trends, may be used depending on the data characteristics (Ly et al., \u003cspan\u003e2021\u003c/span\u003e; Kilibarda et al., \u003cspan\u003e2020\u003c/span\u003e). ArcMap Pro\u0026apos;s Geostatistical Analyst tools will be utilized to perform the Kriging interpolation. This process involves defining the Kriging model parameters based on the variogram analysis and the spatial coordinates of the rain gauge stations (Esri, \u003cspan\u003e2023\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eModel Validation and Accuracy Assessment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe performance of the selected Kriging model was evaluated using cross-validation techniques. This involves splitting the data into training and validation sets. The Kriging model was built using the training data, and then it was applied to predict rainfall values at the validation locations. The predicted values will be compared to the actual observed values to assess the model\u0026apos;s accuracy. Statistical measures, such as Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), will be used to quantify the prediction errors and assess model performance (Ly et al., \u003cspan\u003e2021\u003c/span\u003e; Kilibarda et al., \u003cspan\u003e2020\u003c/span\u003e; Li \u0026amp; Heap, \u003cspan\u003e2014\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eThe following formulas are commonly used to evaluate the performance of geostatistical interpolation models, including Kriging. These metrics help quantify the prediction accuracy by comparing predicted rainfall values with actual observed data during cross-validation (Li \u0026amp; Heap, \u003cspan\u003e2014\u003c/span\u003e; Ly et al., \u003cspan\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRoot Mean Squared Error (RMSE)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRMSE measures the square root of the average squared differences between predicted and observed values:\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e( 1 )\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003e\u0026bull; P\u003csub\u003ei\u003c/sub\u003e = predicted value at location i\u003c/p\u003e\n\u003cp\u003e\u0026bull; O\u003csub\u003ei\u003c/sub\u003e = observed value at location i\u003c/p\u003e\n\u003cp\u003e\u0026bull; n\u0026thinsp;=\u0026thinsp;total number of validation points\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMean Absolute Error (MAE)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMAE measures the average of the absolute differences between predicted and observed values:\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e( 2 )\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003e\u0026bull; P\u003csub\u003ei\u003c/sub\u003e = predicted value at location i\u003c/p\u003e\n\u003cp\u003e\u0026bull; O\u003csub\u003ei\u003c/sub\u003e = observed value at location i\u003c/p\u003e\n\u003cp\u003e\u0026bull; n\u0026thinsp;=\u0026thinsp;total number of validation points\u003c/p\u003e\n\u003cp\u003eOnce the Kriging interpolation is complete, the results was analyzed, and maps depicting the spatial distribution of interpolated rainfall across North East Amhara (Wollo) was generated. High-resolution, visually appealing maps were created using ArcMap Pro\u0026apos;s cartographic tools. Relevant base layers, such as topography, and informative legends will be included to enhance the map\u0026apos;s interpretability and provide context for the rainfall patterns.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSoftware\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eArcMap Pro is the primary software used throughout this project. It employed for data analysis, performing the Kriging interpolation, and generating the spatial interpolation maps.\u003c/p\u003e"},{"header":"Results and discussion","content":"\u003cp\u003e\u003cstrong\u003eEvaluating the Spatial Distribution of Rainfall Gauge Data in North East Amhara (Wollo), Ethiopia\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAssessing the spatial distribution of rainfall gauge data in North East Amhara (Wollo), Ethiopia. The analysis aims to prepare the data for interpolation by examining the completeness and spatial arrangement of the rainfall measurements. This process involves several steps, including data collection, spatial plotting, and exploratory spatial data analysis (ESDA).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCollection and Rearrangement of Rainfall Data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRainfall data is collected from Ethiopian meteorological agencies, covering 55 stationsin the North East Amhara region. Key station details, including town name, wereda, region, zone, mean annual rainfall (RAIN), elevation, latitude (lat), and longitude (log), are recorded. Missing data is identified and addressed using techniques such as data imputation or excluding incomplete records to ensure dataset completeness for further analysis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eExploratory Spatial Data Analysis (ESDA)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eExploratory Spatial Data Analysis (ESDA) is crucial for understanding the spatial characteristics of data prior to interpolation. In this study, ESDA was conducted to inform the selection of appropriate Kriging models for rainfall data in the North East Amhara region, Ethiopia.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eHistogram and Q-Q Plot Analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eExploratory analysis of the rainfall data using a histogram revealed a right-skewed distribution, with a mean of 1,042.54 units and a median of 965.56 units. The skewness indicates a tendency toward higher rainfall values, while the kurtosis value of 2.7 suggests a distribution moderately close to normal. To further assess normality, a Q-Q plot was employed. The plot showed that the central values closely followed a normal distribution, whereas deviations at the tails indicated mild skewness or potential outliers. These findings underscore the importance of data transformation and normalization prior to geostatistical modeling.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Transformation for Normality\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe skewness and kurtosis of the rainfall data were assessed before and after applying a log transformation. The transformation improved the data distribution, bringing it closer to normality. These preprocessing steps are crucial for enhancing the reliability of geostatistical interpolation methods such as Kriging (Li et al., \u003cspan\u003e2022\u003c/span\u003e; Zhang et al., 2021; Ahmed et al., \u003cspan\u003e2023\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eKriging Interpolation Model Selection and Implementation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo estimate the spatial distribution of rainfall in North East Amhara (Wollo), three Kriging techniques Simple Kriging, Ordinary Kriging, and Universal Kriging were applied using ArcMap Pro\u0026rsquo;s Geostatistical Analyst tools. Each model was selected based on underlying assumptions about the mean and spatial variability of the data.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eReview Cross-Validation Results\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCross-validation results were assessed using key statistical metrics to evaluate model performance. The Mean Error indicates bias, where values closer to zero reflect minimal bias (Li \u0026amp; Heap, \u003cspan\u003e2014\u003c/span\u003e; Ly et al., \u003cspan\u003e2021\u003c/span\u003e). The Root Mean Square Error (RMSE) measures overall prediction accuracy, with lower values indicating better performance (Li \u0026amp; Heap, \u003cspan\u003e2014\u003c/span\u003e; Blanchet et al., \u003cspan\u003e2023\u003c/span\u003e). The Mean Standardized Error (MSE) like the mean error, should also be near zero for reliable predictions (Ly et al., \u003cspan\u003e2021\u003c/span\u003e; Kilibarda et al., \u003cspan\u003e2020\u003c/span\u003e). Lastly, the Root Mean Square Standardized Error (RMSSE) is ideally close to one, suggesting an appropriately modeled spatial structure.\u003c/p\u003e\n\u003cp\u003eTable: 2 Cross-Validation Statistics of Kriging Models in ArcMap Pro\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"543\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 24.9541%;\"\u003e\n \u003cp\u003eInterpolation Method\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 9.90826%;\"\u003e\n \u003cp\u003eCount\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.3945%;\"\u003e\n \u003cp\u003eMean Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.7431%;\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.5596%;\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2936%;\"\u003e\n \u003cp\u003eRMSSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16.1468%;\"\u003e\n \u003cp\u003eAvg. Std. Error\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 24.9541%;\"\u003e\n \u003cp\u003eSimple Kriging\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 9.90826%;\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.3945%;\"\u003e\n \u003cp\u003e-4.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.7431%;\"\u003e\n \u003cp\u003e83.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.5596%;\"\u003e\n \u003cp\u003e-0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2936%;\"\u003e\n \u003cp\u003e1.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16.1468%;\"\u003e\n \u003cp\u003e61.21\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 24.9541%;\"\u003e\n \u003cp\u003eOrdinary Kriging\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 9.90826%;\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.3945%;\"\u003e\n \u003cp\u003e5.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.7431%;\"\u003e\n \u003cp\u003e101.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.5596%;\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2936%;\"\u003e\n \u003cp\u003e1.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16.1468%;\"\u003e\n \u003cp\u003e76.68\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 24.9541%;\"\u003e\n \u003cp\u003eUniversal Kriging\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 9.90826%;\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.3945%;\"\u003e\n \u003cp\u003e-6.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.7431%;\"\u003e\n \u003cp\u003e106.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11.5596%;\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2936%;\"\u003e\n \u003cp\u003e1.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16.1468%;\"\u003e\n \u003cp\u003e369.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eBased on the cross-validation metrics, Simple Kriging emerged as the most effective interpolation method among the three models tested. It demonstrated the lowest Root Mean Square Error (83.974) and Average Standard Error (61.210), indicating high predictive accuracy. Additionally, it showed a Mean Error of -4.508 and a Mean Standardized Error of -0.073, both values being closest to zero, suggesting minimal bias. The Root Mean Square Standardized Error (1.334) was also nearest to the ideal value of 1. These combined results clearly indicate that Simple Kriging offers superior performance for spatial interpolation of rainfall in the study area.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAccessing Standard Error Information in Kriging with ArcGIS Pro\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe kriging error map provides a visual representation of the spatial distribution of prediction errors across a region. The map identifies areas where kriging interpolation is more reliable (lighter shades) and where it is less reliable (darker shades). Addressing the high-error zones through additional data collection and refining the kriging model can enhance the overall accuracy and reliability of spatial predictions in this region.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRainfall distribution maps in North East Amhara (Wollo), Ethiopia\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSpatial analysis of rainfall patterns is vital for understanding climatic impacts on agriculture and water resources. In North East Amhara, Wollo, Ethiopia, this analysis highlights areas of varying rainfall, aiding effective resource management and planning (Gebremichael et al., 2014). Figure\u0026nbsp;9 presents the spatial distribution of interpolated rainfall data, crucial for assessing rainfall variability and supporting sustainable development strategies .\u003c/p\u003e\n\u003cp\u003eThe map illustrates a complex pattern of rainfall distribution across northeastern Amhara (Wollo).Low Rainfall Zones The eastern portionof the study area (Oromia Zone,) and eastern Wollo around Kalu displays the lowest rainfall amounts. Northwestern Lows The Waghemra Zone in the northern part of the study area also exhibits a low rainfall pattern. Similar to the eastern zone.\u003c/p\u003e\n\u003cp\u003eSouthwestern Highs In contrast, the southwestern part of the map, potentially within the South Wollo Zone, shows the highest rainfall. This area likely receives over 1,831 mm annually. North Wollo Moderation The north-central part of the map, likely representing North Wollo Zone, displays a moderate rainfall pattern.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRainfall distribution of the study area using Natural break classification scheme\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe \u0026quot;Natural Breaks (Jenks)\u0026quot; Reclassify tool in ArcGIS utilizes the Jenks Natural Breaks classification method to classify data into meaningful intervals. Developed by Jenks in the 1960s, this approach minimizes within-class variance while maximizing between-class variance to identify distinct groupings. ArcGIS automatically calculates breakpoints based on user-defined classes, facilitating the creation of thematic maps that effectively communicate spatial patterns. This tool is widely used in GIS applications for spatial analysis and visualization (Jenks, \u003cspan\u003e1967\u003c/span\u003e; ESRI, n.d.; Steiniger \u0026amp; Hunter, \u003cspan\u003e2013\u003c/span\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003e:Distribution of Rainfall class\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003eNo\u003cbr\u003e\u003c/th\u003e\n \u003cth align=\"left\"\u003eRainfall class\u003cbr\u003e\u003c/th\u003e\n \u003cth align=\"left\"\u003eArea/km2\u003cbr\u003e\u003c/th\u003e\n \u003cth align=\"left\"\u003ePercentage\u003cbr\u003e\u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e1\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003eLow\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"char\"\u003e29053.8\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003e51.9\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e2\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003eMedium\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"char\"\u003e18915.3\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003e33.7\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e3\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003eHigh\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"char\"\u003e8009.1\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003e14.3\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e4\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003eTotal\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"char\"\u003e55978.2\u003cbr\u003e\u003c/td\u003e\n \u003ctd align=\"left\"\u003e100\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe table illustrates the distribution of rainfall classes within a specific area, based on Natural break class In the \u0026quot;Low Rainfall Class,\u0026quot; an expanse of 29,053.8 km2 is accounted for, constituting approximately 51.90% of the total area.The \u0026quot;Medium Rainfall Class\u0026quot; encompasses an area of 18,915.3 km2, representing around 33.79% of the total area.Covering 8,009.1 km2, the \u0026quot;High Rainfall Class\u0026quot; comprises approximately 14.31% of the total area.The total area under consideration sums up to 55,978.2 km2, with each rainfall class contributing distinct proportions to the overall landscape.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study examined rainfall gauge data in North East Amhara (Wollo), Ethiopia, to understand its spatial distribution. The goal was to prepare the data for interpolation, a technique used to estimate rainfall values in areas lacking rain gauges. The project involved collecting data from 55 stations across the region. Details like station name, location, elevation, and annual rainfall were recorded. Missing data was addressed to ensure the data set's completeness.\u003c/p\u003e\u003cp\u003eNext, spatial analysis was conducted using ArcMap Pro. This included adding geographical coordinates to the data and visualizing rainfall patterns on a map with elevation shading. This visualization provided a clearer picture of rainfall distribution in relation to the region's topography. Exploratory Spatial Data Analysis (ESDA) was performed to gain insights into the data's characteristics. Histograms and QQ plots were used to assess the distribution of rainfall values. This analysis revealed a slight skew towards higher rainfall values, indicating that some areas receive significantly more rain than others.\u003c/p\u003e\u003cp\u003eSeveral interpolation techniques, including Simple Kriging, Ordinary Kriging, and Universal Kriging, were considered. Based on cross-validation metrics, Simple Kriging proved to be the most suitable method for this data set. The final analysis focused on the spatial distribution of rainfall across the study area. The results depicted a complex pattern. The eastern portion and eastern Wollo around Kalu displayed the lowest rainfall. The Waghemra Zone in the north also exhibited low rainfall. In contrast, the southwestern part, likely representing South Wollo Zone, received the highest rainfall, exceeding. The north-central part experienced moderate rainfall.\u003c/p\u003e\u003cp\u003eA classification scheme was employed to categorize the spatial distribution of rainfall into low, medium, and high classes. The analysis revealed that the low rainfall class covered the majority of the area (over 50%), followed by the medium rainfall class (around 33%), and lastly, the high rainfall class (approximately 14%).This study provides valuable information about the spatial patterns of rainfall in northeastern Amhara (Wollo). This knowledge can be used for various purposes, such as planning\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbegaz, A., Mekonnen, B., \u0026amp; Tadesse, Y. (2023). \u003cem\u003eSpatiotemporal analysis of rainfall variability and trends in Ethiopia\u003c/em\u003e. Journal of Hydrology: Regional Studies, 45, 101262. https://doi.org/10.1016/j.ejrh.2023.101262\u003c/li\u003e\n\u003cli\u003eAbegaz, A., Teshome, G., \u0026amp; Fenta, A. A. (2024). Rainfall interpolation and trend analysis in the Ethiopian highlands. Climate Risk Management, 39, 100502. https://doi.org/10.1016/j.crm.2024.100502\u003c/li\u003e\n\u003cli\u003eAhmed, A. 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Hydro-climatic hazards and adaptation strategies in Ethiopia. Environmental Research Letters, 20, 034012. https://doi.org/10.1088/1748-9326/acfc2f\u003c/li\u003e\n\u003cli\u003eWorld Meteorological Organization (WMO). (2018). Guide to hydrological practices. Geneva: WMO-No. 168. https://library.wmo.int/\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Rainfall distribution, Spatial analysis, Kriging, GIS, Interpolation, North East Amhara, Climate planning","lastPublishedDoi":"10.21203/rs.3.rs-6457750/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6457750/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBackground: Accurate spatial estimation of rainfall is essential for informed agricultural planning, sustainable water resource use, and climate resilience, particularly in data-scarce regions like North East Amhara (Wollo), Ethiopia.. In North East Amhara (Wollo), Ethiopia, rainfall data is often sparse and unevenly distributed, making it necessary to evaluate the spatial pattern of available rainfall gauge data for accurate interpolation and analysis.\u003cbr\u003e\n Method: This study compiled rainfall data from 55 meteorological stations, incorporating geographic and climatic variables such as mean annual rainfall, elevation, latitude, and longitude. Missing data were addressed to ensure completeness. Spatial distribution was visualized using ArcMap Pro, and Exploratory Spatial Data Analysis (ESDA) was conducted through histogram and Normal QQ plot analysis. To generate continuous rainfall surfaces, three interpolation methods Simple Kriging, Ordinary Kriging, and Universal Kriging were applied and evaluated using cross-validation metrics.\u003cbr\u003e\n Result: Simple Kriging emerged as the most accurate interpolation method. The spatial analysis revealed heterogeneous rainfall distribution, with low rainfall in the eastern and northern zones, high rainfall in the southwest, and moderate rainfall in the north-central region. A classification system was applied to categorize rainfall into low, medium, and high ranges, aiding in regional planning.\u003cbr\u003e\n Conclusion: The findings offer critical insights into the spatial rainfall patterns of North East Amhara and support the development of adaptive strategies such as drought-resistant crops, water-saving techniques, water storage infrastructure, and early warning systems. Long-term rainfall analysis is recommended to strengthen future planning and climate resilience efforts.\u003c/p\u003e","manuscriptTitle":"Simple Kriging for Rainfall Mapping: A Geostatistical Analysis of North East Amhara (Wollo), Ethiopia Using ArcMap Pro.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-17 06:21:49","doi":"10.21203/rs.3.rs-6457750/v1","editorialEvents":[{"type":"communityComments","content":2}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1b04677e-ae5c-4541-8190-607d0c534c62","owner":[],"postedDate":"April 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":47216557,"name":"Climate Analysis and Modeling"},{"id":47216558,"name":"Geographic Information Systems"},{"id":47216559,"name":"Physical Geography"}],"tags":[],"updatedAt":"2025-04-17T06:21:49+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-17 06:21:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6457750","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6457750","identity":"rs-6457750","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}