Kriging in GIS and variogram

Kriging is an advanced spatial interpolation technique used in GIS (Geographic Information System) that estimates values for unknown locations based on the values observed at nearby known locations. It is a geostatistical method that takes into account not only the distances between points but also the spatial correlation or variability in the data.

Unlike simpler interpolation methods like IDW, which assume a constant variation across the study area, kriging incorporates the spatial autocorrelation of the data to produce more accurate and precise estimates. Kriging considers the spatial arrangement and patterns of the data points to generate a surface that honors the underlying spatial structure.

The key principle behind kriging is the variogram, which quantifies the spatial correlation between pairs of points at different distances. The variogram measures how the values of nearby points vary from each other as a function of distance. It provides information about the spatial dependence or variability in the dataset.

The kriging process involves three main steps:

1. Variogram modeling: The first step in kriging is to construct a variogram, which is a plot of the semivariance (a measure of dissimilarity or variability) against distance or lag between pairs of points. The variogram helps to understand the spatial structure of the data and determine the range, sill, and nugget effect. Based on the variogram, a mathematical model is fitted to describe the spatial correlation.

2. Interpolation: Once the variogram is modeled, kriging calculates the weights or coefficients for the known points based on their spatial relationship to the target location. The weights are determined through a process known as kriging equations, which consider the variogram and covariance between points. These equations generate the optimal weights that minimize the prediction error.

- Ordinary Kriging (OK): Assumes a constant mean value across the study area.

- Simple Kriging (SK): Accounts for an unknown mean value, estimating it from the data.

- Universal Kriging (UK): Incorporates additional spatially correlated variables (covariates) in addition to the location coordinates.

3. Prediction: The final step is the estimation of values at the unknown locations using the calculated weights. Kriging provides not only the predicted values but also the estimation error or uncertainty associated with each prediction. This information can be valuable in decision-making processes.

Kriging is particularly useful when dealing with spatial datasets that exhibit spatial autocorrelation, anisotropy (directional dependence), or irregularly spaced points. It provides a more sophisticated approach to spatial interpolation by considering the inherent spatial relationships in the data.

GIS software typically provides various kriging algorithms and tools that allow users to model the variogram, perform the interpolation, and generate kriging predictions and associated error maps.

Comments

History of GIS

1. 1832 - Early Spatial Analysis in Epidemiology: - Charles Picquet creates a map in Paris detailing cholera deaths per 1,000 inhabitants. - Utilizes halftone color gradients for visual representation. 2. 1854 - John Snow's Cholera Outbreak Analysis: - Epidemiologist John Snow identifies cholera outbreak source in London using spatial analysis. - Maps casualties' residences and nearby water sources to pinpoint the outbreak's origin. 3. Early 20th Century - Photozincography and Layered Mapping: - Photozincography development allows maps to be split into layers for vegetation, water, etc. - Introduction of layers, later a key feature in GIS, for separate printing plates. 4. Mid-20th Century - Computer Facilitation of Cartography: - Waldo Tobler's 1959 publication details using computers for cartography. - Computer hardware development, driven by nuclear weapon research, leads to broader mapping applications by early 1960s. 5. 1960 - Canada Geograph...

Supervised Classification

Image Classification in Remote Sensing Image classification in remote sensing involves categorizing pixels in an image into thematic classes to produce a map. This process is essential for land use and land cover mapping, environmental studies, and resource management. The two primary methods for classification are Supervised and Unsupervised Classification . Here's a breakdown of these methods and the key stages of image classification. 1. Types of Classification Supervised Classification In supervised classification, the analyst manually defines classes of interest (known as information classes ), such as "water," "urban," or "vegetation," and identifies training areas —sections of the image that are representative of these classes. Using these training areas, the algorithm learns the spectral characteristics of each class and applies them to classify the entire image. When to Use Supervised Classification: - You have prior knowledge about the c...

Representation of Spatial and Temporal Relationships

In GIS, spatial and temporal relationships allow the integration of location (the "where") and time (the "when") to analyze phenomena across space and time. This combination is fundamental to studying dynamic processes such as urban growth, land-use changes, or natural disasters. Key Concepts and Terminologies Geographic Coordinates : Define the position of features on Earth using latitude, longitude, or other coordinate systems. Example: A building's location can be represented as (11.6994° N, 76.0773° E). Timestamp : Represents the temporal aspect of data, such as the date or time a phenomenon was observed. Example: A landslide occurrence recorded on 30/07/2024 . Spatial and Temporal Relationships : Describes how features relate in space and time. These relationships can be: Spatial : Topological (e.g., "intersects"), directional (e.g., "north of"), or proximity-based (e.g., "near"). Temporal : Sequential (e....

GIS: Real World and Representations - Modeling and Maps

Geographic Information Systems (GIS) serve as a bridge between the real world and digital representations of geographic phenomena. These representations allow users to store, analyze, and visualize spatial data for informed decision-making. Two key aspects of GIS in this context are modeling and maps , both of which are used to represent real-world geographic features and phenomena in a structured, analyzable format. Let's delve into these concepts, terminologies, and examples in detail. 1. Real World and Representations in GIS Concept: The real world comprises physical, tangible phenomena, such as landforms, rivers, cities, and infrastructure, as well as more abstract elements like weather patterns, population densities, and traffic flow. GIS allows us to represent these real-world phenomena digitally, enabling spatial analysis, decision-making, and visualization. The representation of the real world in GIS is achieved through various models and maps , which simplify...

History of GIS

The history of Geographic Information Systems (GIS) is rooted in early efforts to understand spatial relationships and patterns, long before the advent of digital computers. While modern GIS emerged in the mid-20th century with advances in computing, its conceptual foundations lie in cartography, spatial analysis, and thematic mapping. Early Roots of Spatial Analysis (Pre-1960s) One of the earliest documented applications of spatial analysis dates back to 1832 , when Charles Picquet , a French geographer and cartographer, produced a cholera mortality map of Paris. In his report Rapport sur la marche et les effets du choléra dans Paris et le département de la Seine , Picquet used graduated color shading to represent cholera deaths per 1,000 inhabitants across 48 districts. This work is widely regarded as an early example of choropleth mapping and thematic cartography applied to epidemiology. A landmark moment in the history of spatial analysis occurred in 1854 , when John Snow inv...

Vineesh V, Geography

Search This Blog