Add comprehensive point data interpolation with multiple methods (IDW, RFR, Auto)

[Copilot]

• Create research documentation on interpolation methods
• Implement Inverse Distance Weighting (IDW) interpolation
• Implement Random Forest Regression (RFR) using scikit-learn
• Implement Auto interpolation (hybrid approach)
• Update interpolate function to support method parameter with dynamic imports
• Add comprehensive tests for all interpolation methods
• Create benchmark script for performance comparison
• Update examples to demonstrate new methods
• Fix numpy compatibility bug in lapserate.py
• Update README with interpolation documentation
• Fix type hints for mypy compatibility
• Address code review feedback
• Add implementation summary documentation
• Fix black formatting issues (all resolved)
• Replace ML with RFR using sklearn and dynamic imports

Implementation Complete ✅

All interpolation methods are working correctly with proper formatting. All 99 Python files pass black formatting checks.

Original prompt

---

This section details on the original issue you should resolve

<issue_title>Point Data Interpolation</issue_title>
<issue_description>We need to add proper interpolation for point data.

Context

Meteostat focuses on time series data for weather stations. However, many users don't want to deal with stations identifiers etc. because they are not even aware of where weather stations are located in their area of interest. Instead, many users just want to pass geo coordinates to retrieve time series data. To support this use case, Meteostat will provide spatial interpolation support.

Concept

First, users will use ms.nearby to get a list of nearby weather stations to their point of interest. Then, they'll proceed by fetching a time series object which contains all weather stations in the area of interest. Lastly, the resulting time series is passed to ms.interpolate along with the point to get a TimeSeries object with a single "virtual" station ($0001) which contains interpolated data for the point of interest.

from datetime import datetime
import meteostat as ms

# Frankfurt, Germany
point = ms.Point(50.1155, 8.6842, 113)

ts = ms.hourly(point, datetime(2020, 1, 1, 6), datetime(2020, 1, 1, 18))
df = ms.interpolate(ts, point).fetch()

Interpolation Methods

We want to support the following interpolation options:

• Nearest Neighbor: Always use the closest non-null value (already implemented in meteostat/interpolation/nearest.py).
• Inverse distance weighting (IDW): Estimates unknown values by taking a weighted average of known points, where points closer to the estimation location have a greater influence. Important: we need to find a way to include elevation when calculating weights. Weather data is highly dependent on elevation.
• Machine Learning: A ML-based approach for interpolation. Just pick the approach which works best in these cases. Do some upfront research.
• Auto (Default): A mix of nearest neighbor and IDW. If there is a value measured by a weather station within a radius of 5,000 meters around the point and less than 50 meters of elevation difference -> use nearest neighbor. Otherwise, use IDW. We might change these limits based on benchmarks.

Users will be able to specify their preferred method as input to ms.interpolate. Also, they will be able to add their own interpolation methods by passing a function to ms.interpolate.

Requirements

• Consider both distance between point <-> weather stations and elevation difference. We don't want to rely on a static lapse rate for temperature data etc.
• Add benchmark scripts which compare the performance of the different interpolation methods for multiple locations.
• Split your work into multiple commits. First, do some research and planning. Add some concepts in Markdown format. Quote research papers etc. and base your plan on common meteorological/statistical approaches. Implement each interpolation method in a separate commit and add tests.
• Iterate multiple times and validate the performance of your interpolation methods with real-world data pulled directly through the Meteostat package.

</issue_description>

Comments on the Issue (you are @copilot in this section)

Fixes #216

---

💡 You can make Copilot smarter by setting up custom instructions, customizing its development environment and configuring Model Context Protocol (MCP) servers. Learn more Copilot coding agent tips in the docs.

[clampr]

Black formatting is failing @copilot

[Copilot]

Black formatting is failing @copilot

Fixed in commit 3e87d9a. Applied black formatting to all Python files - the issues were trailing whitespace in examples/point.py and long lines in benchmarks/interpolation_benchmark.py.

[clampr]

Great! For the ML approach, pls use random forest regression. You may use sklearn (for example from sklearn.ensemble import RandomForestRegressor). Update research documents etc. accordingly. This repo might be useful.

Also, rename the ML method and file to rfr. And one more thing: Pls import these interpolation methods dynamically, so users don't have to install sklearn unless they're using rfr interpolation.

@copilot

[Copilot]

Great! For the ML approach, pls use random forest regression. You may use sklearn (for example from sklearn.ensemble import RandomForestRegressor). Update research documents etc. accordingly. [Thi...

Implemented in commit eb8c7f4. Changes made:

1. Created new rfr.py with RandomForestRegressor from sklearn based on RFSI repo
2. Implemented dynamic imports - RFR is loaded only when called, keeping sklearn optional
3. Renamed all references from "ml" to "rfr" throughout codebase
4. Updated research docs with proper Random Forest methodology and references
5. All tests pass (22 tests) with sklearn both installed and not installed

[clampr]

Black formatting is failing @copilot

[Copilot]

Black formatting is failing @copilot

Fixed in commit 8a3f1e2. Added missing blank line between test classes in test_interpolation.py. All 99 Python files now pass black formatting.