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Taylor Diagram Excel

How to do Taylor Diagram in Excel?

First of all, before further descriptions about Taylor Diagram, it is necessary to respond that we cannot draw Taylor Diagram in Excel. The Taylor diagram can represent three different statistics simultaneously. So it is not a simple graph. You can calculate the different components' values of the Taylor Diagram in Excel - RMSE (Root Mean Square Error)/RMSD (Root Mean Square Difference), standard deviation, and R Pearson correlation - but you can't draw Taylor Diagram in Excel. For better understanding and get more knowledge about Taylor Diagram, it is better to study the following statements:

Taylor (2001) has constructed a significant diagram that statistically quantifies the degree of similarity between two fields. One field will be called the "reference" field, usually representing some observed state. The other area will be referred to as a "test" field (typically a model-simulated field). The aim is to quantify how closely the test field resembles the reference field.

Taylor Diagram can concisely summarize the degree of correspondence between simulated and observed patterns, variables, or fields. On the Taylor Diagram, the correlation coefficient and the root-mean-square (RMS) difference between the two variables, along with the ratio of the standard deviations of the two patterns, are all indicated by a single point on a two-dimensional (2-D) plot. Together, these statistics provide a quick summary of the degree of pattern correspondence, allowing one to measure how accurately a model simulates the natural system. The diagram is particularly beneficial in assessing the relative merits of competing models and in monitoring whole performance as a model evolves (Taylor, 2001).

Different researchers have tried to depict Taylor Diagram with various coding and programming languages, such as NCL, MATLAB, and R packages. But it is necessary to know that we cannot draw Taylor Diagram in Excel. Taylor Diagram is a professional and unique graph that includes three main statistical components, namely RMSE (Root Mean Square Error)/RMSD (Root Mean Square Difference), standard deviation, and R Pearson correlation.

  • The R (Pearson Correlation) is needed to indicate the extent to which patterns in the predicted data match those in the observation data. It is referred to as Pearson's correlation or simply as the correlation coefficient. Correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and precipitation values. Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables. If the relationship between the variables is not linear, then the correlation coefficient does not adequately represent the strength of the relationship between the variables.
    Pearson's R can range from -1 to 1. A correlation coefficient of 1 means that data lie on a perfect straight line with a positive slope. A correlation coefficient of -1 means that data lie on a perfect straight line with a negative slope. Zero means that no linear relationship between the variables.
  • Key Point 1: In the Taylor Diagram the value of R has located between 0 and 1.
  • RMSE (Root Mean Square Error): Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). Root Mean Square Error (RMSE) is a standard way to measure the error of a model in predicting quantitative data. RMSE tells us how located the data is around the line of best fit. Root mean square error is commonly used in climatology, forecasting, and regression analysis to verify experimental results.
  • Key Point 1: It is important to know that when standardized observations and forecasts are used as RMSE inputs, there is a direct relationship with the correlation coefficient. In other words, if the R Pearson is 1, the RMSE will be 0, because all of the points lie on the regression line, indeed there are no errors.
  • Key Point 2: The RMSE is thus the distance, on average, of a data point from the fitted line, measured along a vertical line.
  • Key Point 3: The RMSE is directly interpretable in terms of measurement units, and so is a better measure of goodness of fit than a correlation coefficient.
  • Standard deviation: The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. The standard deviation is a measure of the spread of scores within a set of data. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation. Generally, calculating standard deviation is valuable any time it is desired to know how far from the mean a typical value from a distribution can be.
  • Key Point 1: Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ. Conversely, a higher standard deviation indicates a wider range of values.
  • Key Point 2: The standard deviation is used in conjunction with the mean to summarize continuous data, not categorical data. In addition, the standard deviation, like the mean, is normally only appropriate when the continuous data is not significantly skewed or has outliers.
  • Key Point 3: Standard deviation is widely used in experimental and industrial settings to test models against real-world data. Also it is used in weather to determine differences in regional climate.

Reference:

Taylor, K.E.2001. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res., 106, 7183-7192, 2001 (also see PCMDI Report 55, http://www-pcmdi.llnl.gov/publications/ab55.html)

Nasrin Salehnia, Narges Salehnia, Sohrab Kolsoumi, Ahmad Saradari Torshizi. 2020. Rainfed wheat (Triticum aestivum L.) yield prediction using economical, meteorological, and drought indicators through pooled panel data and statistical downscaling. Ecological Indicators, 11:105991,Rainfed wheat yield

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