How to calaculate Statistical mono window (SMW) algorithm coefficients for LST?

20 December 2022 1 9K Report

I'm attempting to understand how the statistical mono window (SMW) algorithm coefficients are computed but it is unclear. I am following Sofia Ermida's paper but facing difficulties in understanding. Could anyone please help in this regard?

Is there any code available to calculate SMW coefficients?

Is it possible to apply the SMW algorithm for Landsat 9 to calculate LST?

Mohamad Dzul Syakimin Mohd Noor

The statistical mono window (SMW) algorithm is a method for estimating the land surface temperature (LST) from satellite imagery. It works by fitting a linear regression model to the relationship between the brightness temperature of the land surface measured by the satellite and the LST.

The coefficients of the SMW algorithm are computed using the following steps:

Collect a set of ground-truth LST measurements and corresponding satellite brightness temperature measurements for a given region.

Divide the data into two sets: a training set and a validation set. The training set is used to fit the linear regression model, while the validation set is used to evaluate the performance of the model.

For each pixel in the training set, compute the brightness temperature and the LST.

Fit a linear regression model to the training data using the brightness temperature as the predictor variable and the LST as the response variable.

Use the linear regression model to predict the LST for each pixel in the validation set, and compare the predicted values to the actual LST values to compute the mean absolute error (MAE) and the root mean square error (RMSE).

Iterate over a range of window sizes and fit the linear regression model using only the data within each window. Compute the MAE and RMSE for each window size and choose the window size that gives the lowest error. This window size is the optimal window size for the SMW algorithm.

Use the optimal window size to fit the final linear regression model and compute the coefficients of the model. These coefficients can then be used to estimate the LST for any given satellite brightness temperature measurement.

It is possible to apply the SMW algorithm to Landsat 9 data to calculate LST. However, you will need to follow the steps outlined above and use the appropriate bands and coefficients for Landsat 9 data. The specific bands and coefficients used may vary depending on the specific Landsat 9 product and the sensor used to collect the data.

I hope this helps! Let me know if you have any further questions.

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