# What is the quantile mapping method as a bias correction approach?

Quantile mapping is a statistical bias correction technique used to adjust climate model outputs to better match observed data. This method is particularly useful in climate science and hydrology for correcting systematic biases in simulated data, such as temperature or precipitation, from climate models.

#### Bias Correction Tool for CMIP6 Data | Example on CanESM5 Model

Key Features of Quantile Mapping:

1. Bias Correction: Quantile mapping adjusts the cumulative distribution function (CDF) of the model output to match the CDF of the observed data.

2. Distribution-Based: It corrects biases across the entire distribution of data, not just mean values. This makes it effective for correcting extreme values (e.g., heavy rainfall or heatwaves).

3. Non-Parametric and Parametric Options: Quantile mapping can be applied in a non-parametric manner (using empirical distributions) or parametric manner (fitting specific probability distributions).

Steps Involved in Quantile Mapping:

1. Develop CDFs: Construct the cumulative distribution functions for both observed and model-simulated data. This involves ranking the data and calculating the probability of each data point.

2. Quantile Matching: For each quantile in the model-simulated data, find the corresponding quantile in the observed data. This step essentially involves mapping the simulated values to the observed values.

3. Apply Corrections: Adjust the model-simulated data using the quantile mapping relationship established in the previous step. This can be done through an interpolation process where model values are adjusted to match the observed quantiles.

Example Process:

1. Observed Data CDF: Calculate the CDF for the observed data (e.g., rainfall measurements).

2. Model Data CDF: Calculate the CDF for the model-simulated data.

3. Mapping Function: Create a mapping function that adjusts model data to match the observed data at each quantile.

4. Apply to Future Projections: Use this mapping function to adjust future climate projections from the model, making them more consistent with historical observations.

- Improves Accuracy: By correcting biases across the entire distribution, quantile mapping can significantly improve the accuracy of climate model outputs.

- Handles Extremes: It is particularly effective in adjusting for extreme events, which are crucial in impact studies.

- Flexibility: The method can be applied using various distributions, allowing flexibility in how biases are corrected.

Limitations:

- Stationarity Assumption: Quantile mapping assumes that the relationship between observed and simulated data remains constant over time, which may not always be true under changing climate conditions.

- Data Requirement: Requires a substantial amount of historical observed data to accurately construct the CDFs.

Applications:

- Climate Change Studies: Used to correct biases in temperature, precipitation, and other climate variables in climate change impact assessments.

- Hydrological Modeling: Applied to correct inputs (e.g., precipitation and temperature) to hydrological models for better water resource management predictions.

- Weather Forecasting: Helps in improving the accuracy of weather forecasts by adjusting model outputs to better match observed weather patterns.

The quantile mapping is a powerful bias correction method that enhances the reliability of climate model outputs by aligning their statistical properties with those of observed data, making it a valuable tool in climate science and related fields.

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