When conducting multi-factor overlay analysis or multi-index comprehensive evaluation, a common preliminary step is to standardize a collection of raster layers from various sources to a uniform 0 to 1 range. This normalization facilitates subsequent weighted overlay procedures. Theoretically, a simple linear rescaling based on the minimum and maximum values of each raster should yield results exactly between 0 and 1.

However, many users encounter a perplexing issue when using tools like QGIS's Raster Rescale tool, the Raster Calculator, or GDAL's gdal_translate command. The resulting raster's minimum and maximum values are almost, but not quite, 0 and 1. For instance, you might expect a range of 0 to 1, but the actual statistics show values like 0.006 to 0.88, or 0 to 0.99999999999999. This discrepancy can be unsettling. Drawing insights from a relevant discussion on GIS Stack Exchange, this article explores the underlying reasons for this issue and presents a more reliable workflow.

Root Causes of the Inaccuracy

While the problem manifests as "incorrect min/max values after rescaling," its origin lies primarily in two factors.

First, linear scaling relies on accurate source raster minimum and maximum values. If the rescaling tool (like gdal_translate with -scale) uses approximate statistics—perhaps manually entered or based on quick-look values from layer properties, rather than the true, computed statistics of the raster—the output will inevitably deviate from expectations. This is why the first recommendation in the Stack Exchange answer is to re-examine the source raster's statistics using gdalinfo.

Second, raster calculations operate within the floating-point number space, which inherently has precision limitations. Even if you provide the exact theoretical minimum and maximum values, the computed results may not be precisely 0 or 1 due to how floating-point arithmetic works. You might obtain a very small negative number or a value like 0.99999999999999. Mathematically, these are practically 0 and 1, but their appearance in a GIS software's attribute table can be misleading, causing users to mistakenly believe the scaling process failed.

A Robust Workflow for Accurate Rescaling

Based on the insights from the forum discussion, here is a more reliable procedure applicable to both command-line environments and QGIS's graphical interface.

Step 1: Obtain Precise Source Statistics with gdalinfo

First, use gdalinfo with the -stats flag to retrieve the true minimum and maximum values of the source raster.

Example command:

gdalinfo REM__IDW.tif -stats

In the metadata section of the output, you'll find information like this:

STATISTICS_MAXIMUM=53.368576049805
STATISTICS_MINIMUM=-1.4455108642578

The STATISTICS_MINIMUM and STATISTICS_MAXIMUM values are the accurate numbers required for the rescaling step. It's best practice to copy these values directly to avoid transcription errors.

Step 2: Perform Linear Rescaling with gdal_translate

Use the gdal_translate command with the -scale option, inputting the exact statistics obtained in Step 1.

Example command:

gdal_translate -scale -1.4455108642578 53.368576049805 0 1 \
  REM__IDW.tif scaled.tif

This command maps the source raster's minimum value (-1.4455) to the target minimum (0) and its maximum value (53.3686) to the target maximum (1). All other pixel values are linearly interpolated between 0 and 1. Note that -scale is followed by four numbers: source_min, source_max, dest_min, dest_max.

Step 3: Verify the Rescaled Statistics

Check the statistics of the output raster to confirm the scaling result.

Example command:

gdalinfo scaled.tif -stats

The test results typically show a minimum value around -2.2551405187698e-16 and a maximum around 0.99999999999999. While the minimum isn't exactly zero, its magnitude is negligible, representing a minor floating-point error. For most GIS analysis and cartographic purposes, such an error is insignificant and can be safely ignored.

Step 4 (Optional): Fine-tune with the -exponent Parameter

If you desire the range to be even closer to [0, 1], you can use the -exponent parameter. According to GDAL documentation, applying an exponent transformation can subtly "compress" the value range. Using an exponent of 1.0 theoretically applies no change but can sometimes help in nudging values closer to the boundaries.

Example command:

gdal_translate -scale -1.4455108642578 53.368576049805 0 1 \
  REM__IDW.tif scaled2.tif -exponent 1

Re-checking the statistics might show the minimum as exactly 0, while the maximum remains 0.99999999999999. This value is effectively 1 for computational and practical applications.

For users preferring QGIS's graphical interface, the GDAL Translate tool (found in the Processing Toolbox) can be used. Simply populate the input file, output file, and scaling parameters (-scale and optionally -exponent) in the "Additional command-line parameters" field or the respective GUI options.

Step 5: Using QGIS Raster Calculator for Simple Cases

For quick validations within QGIS, you can manually perform the linear scaling using the Raster Calculator. The expression would be:

("REM__IDW@1" - (-1.4455108642578)) / (53.368576049805 - (-1.4455108642578))

Here, REM__IDW@1 refers to the first band of the input raster. The expression subtracts the minimum value from each cell and divides by the total range. After calculation, checking the layer properties will reveal statistics very close to 0 and 1, subject to the same floating-point precision mentioned earlier.

Alternative Approaches

Beyond using gdal_translate -scale, two other methods are commonly used:

  • QGIS Raster Calculator Modeling: Encapsulate the linear expression shown in Step 5 into a reusable QGIS model or script. This approach is user-friendly for those who prefer a graphical interface and integrates well with subsequent geoprocessing steps like weighted overlay or reclassification.
  • Controlling Output Data Type: After scaling to a 0-1 range, consider saving the output as a Float32 data type. This maintains sufficient precision while avoiding the larger file sizes associated with Float64. If subsequent steps only require integer classes (e.g., for suitability zones), you could further process the raster to integer type.

Regardless of the method, two key takeaways remain: always base your scaling on true statistical values, and understand that floating-point precision errors are normal and negligible.

Conclusion

The issue of QGIS raster rescaling producing "inaccurate" results is typically not a fault of the tools themselves, but rather a consequence of using approximate source statistics combined with the inherent limitations of floating-point arithmetic. By first obtaining precise statistics with gdalinfo and then applying them in gdal_translate with the -scale (and optionally -exponent) parameter, you can reliably generate normalized rasters with a stable 0-1 range.

For GIS analysts involved in multi-criteria decision making or suitability modeling, understanding this workflow ensures confidence in your data preparation and prevents unnecessary concern over minuscule numerical discrepancies. If you have developed other effective techniques for raster normalization in QGIS or have insights on handling floating-point precision, please share them in the comments.