Spatial Interpolation-kerkin interpolation and interpolation of kerkin

Spatial Interpolation-kerkin interpolation and interpolation of kerkin

The Kerry kingfa is an advanced statistical process that generates an estimated surface through a group of Scattered Points with z values. Unlike other interpolation methods in the interpolation tool set, before selecting the best estimation method used to generate the output surface, we effectively use the kerkin tool to study the interaction of spatial behavior involving the phenomenon of z-value representation.

What is kerkingfa?

IDW (Inverse Distance weighting method) and splines value insertion tools are called deterministic interpolation methods because these methods are directly based on the surrounding measurements or specify mathematical formulas that determine the smoothness of the surface. The second type of interpolation method is composed of the geographic statistical method (for example, the Keli-jin method). This method is based on a statistical model that contains self-correlation (that is, the statistical relationship between measurement points. Therefore, the local statistical method not only provides the ability to generate a prediction surface, but also provides a certain degree of certainty or accuracy for prediction.

The kerkin method assumes that the distance or direction between the sampling points can reflect the spatial correlation that can be used to describe the surface changes. The kerkin tool fits mathematical functions with a specified number of points or all points within a specified radius to determine the output value for each position. The kerkin method is a multi-step process that includes exploratory statistical analysis of data, variant function modeling, and surface creation, as well as the study of variance surface. When you understand the spatial distance or direction deviation in the data, you will think that the kerkin method is the most suitable method. This method is usually used in Soil Science and geology.

Kerry kingfa Formula

Because the kerkin method can weight the surrounding measurements to predict the unmeasured position, it is similar to the inverse distance weight method. The common formulas of the two interpolation machines are composed of the weighted sum of the data:

• Where:

  Z (si)= NthIMeasured value at location

  Lambda I= NthIUnknown weights of measured values at locations

  S0= Predicted location

  N= Number of measured values

In the anti-distance weight method, the weightLambda IIt depends only on the distance of the predicted position. However, when using the kerkin method, the weight not only depends on the distance between measurement points, the predicted position, but also the overall spatial arrangement based on the measurement points. To use space arrangement in weights, you must quantify the Space Self-correlation. Therefore, in the common Kerry kingfa, the weightLambda IA fitting model that depends on the measurement point, the distance between the predicted location, and the spatial relationship between the measured values around the predicted location. The following sections describe how to create a prediction surface map and a prediction accuracy map using the commonly used kerkin formula.

Use the kerkin method to create a prediction surface map

Two tasks are required to use the kerkin interpolation method for prediction:

• Locate the dependency rule.
• Make predictions.

To implement these two tasks, kerkingfa has to go through two steps:

Because the two tasks are different, it can be determined that the Kerry kingfa uses two data records: the first is the spatial self-correlation of the estimated data, and the second is the prediction.

Mutation analysis

Fitting Model or spatial modeling is also called structural analysis or variant analysis. In Spatial Modeling of measurement point structure, the following equations are used for calculation of all location pairs separated by distance h starting with an empirical semi-variant function:

Semivariogram(distance

H

) = 0.5 * average{(value

I

 – value

J

}

2

]

This formula involves calculating the difference square of the matching position.

Displays the pairing of a vertex (red dot) with all other measurement positions. This process is performed on each measurement point.

Calculates the difference square of the matching position.

Generally, the distance between each location is unique and there are many points. It is difficult to quickly draw all pairs. Instead of drawing each pair, the pair is grouped into individual step-size bar units. For example, calculate the mean semi-variance of all vertices greater than 40 m but less than 50 m. The empirical semi-mutations function represents the average semi-mutations on the y axis, and the distance or step size on the x axis (see ).

Sample empirical semi-variant function Diagram

The following basic principle is used to quantify the correlation between null and null: Closer things are more similar than those that are far away. Therefore, the closer the location pair is (on the leftmost side of the x axis of the semi-variant function cloud ), values should be more similar (lower on the y axis of the semi-variant function cloud ). The farther the distance from the location pair is (moving to the right on the x axis of the semi-variant function cloud), the more different it should be, the square of the difference will be higher (move up on the y axis of the semi-variant function cloud ).

Model fitting based on empirical semi-variant Functions

The next step is to build a point fitting model based on the empirical semi-variant function. Semi-variant function modeling is a key step between spatial description and spatial prediction. The main application of the kerkin method is to predict the attribute values at unsampled locations. The empirical semi-variant function provides spatial self-related information about datasets. However, it does not provide all possible directions and distances. Therefore, to ensure that the kerkin variance predicted by the kerkin method is positive, it is necessary to fit the model (I .e. continuous function or curve) based on empirical semi-variant functions. This operation is theoretically similar to regression analysis, where continuous lines or curves are fitted based on data points.

To fit the model based on the empirical semi-variant function, select the function used as the model (for example, the spherical type that rises at the beginning and becomes horizontally when the distance is greater than a certain range) (See the following spherical model example ). The points on the empirical semi-variant function are somewhat different from the model. Some points are above the model curve and some are below the model curve. However, if you add a corresponding distance, each vertex will be online above, or if you add another corresponding distance, each vertex will be online below, the two distance values should be similar. Multiple semi-variant function models are available.

Semi-variant function model

The Kerry kingfa tool provides the following functions from which you can select functions used for modeling empirical semi-variant functions:

• Circle
• Sphere
• Index
• Gaussian
• Linear

The selected model affects the prediction of unknown values, especially when the curves close to the origin are obviously different. The steep the curve near the origin, the greater the influence of the nearest adjacent element on the prediction. In this way, the output surface will not be smooth. Each model is used to more accurately fit different types of phenomena.

Two common models are displayed and the differences between functions are determined:

Spherical model example

This model shows the process of gradually decreasing spatial self-correlation (equivalent to increasing semi-variance) to zero self-correlation after a certain distance is exceeded. The spherical model is one of the most common models.

Spherical model example

Exponential model example

This model is used exponentially to reduce the space self-correlation with the increase of distance. Here, the self-correlation will only disappear completely from infinity. The exponential model is also a common model. Which model should be used based on the prior knowledge of spatial self-correlation and data phenomena of data.

Exponential model example

For more information about mathematical models, see the following.

Measure the test taker's knowledge about the semi-variant function-variable process, base station, and block fund.

As mentioned above, the semi-variant function shows the spatial self-correlation of the measurement sample points. Due to the basic principle of geography (The Closer things are, the closer they are), the difference square of the close measurement point is usually smaller than the difference square of the Far Measurement Point. The positions are adjusted and then the model is fitted based on these positions. The change process, base table, and block gold are usually used to describe these models.

Change Process and Base Station

When you view the model of the semi-variant function, you will notice that the model shows a horizontal state at a specific distance. The distance between the first time the model shows a horizontal state is called a change process. The sample location separated by the distance near the change is related to the spatial self-correlation, while the sample location farther away from the change is not related to the spatial self-correlation.

Change process, base station and block gold illustration

The value obtained by the semi-variant function model in the variable path (the value on the y axis) is called the base station. The base station is equal to the base station minus the block gold. The block is described in the following sections.

Block gold

Theoretically, the value of the semi-variant function is 0 at zero spacing (for example, step size = 0. However, at an infinitely small distance, the semi-variant function usually shows the block gold effect, that is, the value is greater than 0. If the intercept of the semi-variant function model on the y axis is 2, the block size is 2.

The block effect can be attributed to the measurement error or the spatial variation source (or both) smaller than the sampling interval ). Measurement errors may occur due to inherent errors in the measurement device. Natural phenomena can change with the change in the proportion range. The slight scale change smaller than the sample distance is shown as part of the block gold effect. Before collecting data, it is very important to understand the proportion of space changes that interest you.

Prediction

Find the correlation or self-correlation in the data (see the Variation Analysis Section above) and complete the first data application (that is, use the spatial information in the data to calculate the distance and perform spatial self-correlation modeling ), you can use a fitting model for prediction. Then, the empirical semi-variant function will be removed.

Now you can use this data for prediction. Similar to the inverse distance weight method, the Kerry method generates weights based on the surrounding measurements to predict unmeasured locations. Same as interpolation by the inverse distance weight method, this method is most affected by the measured value closest to the unmeasured position. However, the kerkin weight of the surrounding measurement point is more complex than the inverse distance weight method. The anti-distance weight method uses a simple distance-based algorithm. However, the weight of the kerkin method is derived from the semi-variant function developed by viewing the spatial features of data. To create a continuous surface of a phenomenon, each location or unit center in the study area (which is arranged based on the semi-variant function and the space of nearby measurements) is predicted.

Kerkin Method

There are two Kingdom methods: the common Kingdom method and the extensive Kingdom method.

The common kerkin method is the most common and widely used method. It is a default method. This method assumes a constant and unknown average value. If we cannot come up with scientific justification, this is a reasonable assumption.

The pan Keri method assumes that there is a coverage trend in the data. For example, we can use deterministic functions (polynomials) to create a model. The polynomial is deducted from the original measurement point, and the auto correlation is modeled by a random error. After fitting the model by random error deviation, before prediction, the polynomial is added back to Prediction to produce meaningful results. This method should be available only when you understand a certain trend in the data and can provide scientific judgment to describe the fankeri method.

Semi-variant function graphics

Kerry kingfa is a complex process that requires more knowledge about spatial statistics than is described in this topic. Before using the kerkin method, you should fully understand its basic knowledge and evaluate the suitability of the data that uses this technology for modeling. If you do not fully understand the process, it is strongly recommended that you view some of the bibliography listed at the end of this topic.

Based on the regionalization variable theory, the kerkin method assumes that spatial changes in phenomena represented by the z value are consistent across the entire surface in terms of statistical significance (for example, the same variation pattern can be observed at all locations on the surface ). The assumption of spatial consistency is very important for the variable theory of regionalization.

Mathematical Model

The following are common shapes and equations used to describe the semi-variance mathematical model.

Spherical semi-variance model illustration

Circle semi-variance model illustration

Exponential semi-variance model illustration

Gaussian semi-variance model illustration

Linear semi-variance model illustration