Interpolating Sparse Yield Monitor Data with Kriging

Interpolating sparse yield monitor data with Kriging requires fitting a spatial variogram to irregular point observations, then predicting values across a regular grid using Ordinary or Universal Kriging. In Python, this pipeline is reliably built with pykrige, geopandas, and rasterio. Unlike deterministic methods (IDW, spline), Kriging explicitly models spatial autocorrelation, quantifies prediction uncertainty, and handles irregular sampling gaps—making it the statistical standard for Spatial Interpolation for Yield Data. Because the algorithm relies on Euclidean distance, you must project coordinates to a local metric CRS before modeling, and you must validate variogram parameters against field-scale spatial structure.

Environment & Dependency Matrix

Critical constraint: Kriging assumes second-order stationarity. Sparse yield datasets frequently exhibit trend drift from soil gradients, elevation changes, or management zones. If your experimental variogram shows a continuous upward slope without reaching a sill, switch to Universal Kriging or detrend the data using a polynomial surface before interpolation. Always validate automated fits against agronomic knowledge; routines frequently overestimate range on sparse datasets.

Production-Ready Pipeline

The script below loads sparse yield points, projects to a metric CRS, fits a spherical variogram, executes Ordinary Kriging, and exports a dual-band GeoTIFF (prediction + variance). For coordinate system selection, consult the official GeoPandas projection guide to identify your field’s correct UTM zone.

import numpy as np
import geopandas as gpd
import rasterio
from rasterio.transform import from_origin
from rasterio.crs import CRS
from pykrige.ok import OrdinaryKriging

# 1. Load & clean sparse yield points
df = gpd.read_file("sparse_yield_points.csv")
gdf = gpd.GeoDataFrame(
    df, 
    geometry=gpd.points_from_xy(df.lon, df.lat), 
    crs="EPSG:4326"
)
gdf = gdf.dropna(subset=["yield_bu_ac"])

# 2. Project to local UTM (metric distances required)
# Replace 32615 with your field's correct UTM zone
gdf_proj = gdf.to_crs("EPSG:32615")
x = gdf_proj.geometry.x.values
y = gdf_proj.geometry.y.values
z = gdf_proj["yield_bu_ac"].values.astype(np.float64)

# 3. Define output grid resolution (10m standard for prescription maps)
grid_res = 10.0
xmin, ymin, xmax, ymax = gdf_proj.total_bounds
cols = int(np.ceil((xmax - xmin) / grid_res))
rows = int(np.ceil((ymax - ymin) / grid_res))
grid_x = np.arange(xmin, xmax, grid_res)
grid_y = np.arange(ymin, ymax, grid_res)

# 4. Run Ordinary Kriging with auto-fitted spherical variogram
ok = OrdinaryKriging(
    x, y, z,
    variogram_model="spherical",
    verbose=False,
    enable_plotting=False,
    nlags=12,
    weight=True
)
z_interp, ss = ok.execute("grid", grid_x, grid_y)

# 5. Export to GeoTIFF (Band 1: Yield, Band 2: Prediction Variance)
transform = from_origin(xmin, ymax, grid_res, grid_res)
with rasterio.open(
    "yield_kriged.tif",
    "w",
    driver="GTiff",
    height=rows,
    width=cols,
    count=2,
    dtype=z_interp.dtype,
    crs=gdf_proj.crs,
    transform=transform,
    nodata=np.nan
) as dst:
    dst.write(z_interp, 1)
    dst.write(ss, 2)

Performance note: pykrige scales at O(n³) due to matrix inversion. For datasets exceeding 10,000 points, either spatially subsample using gdf.sample() or migrate to gstools/scikit-gstat for sparse matrix solvers. See the pykrige documentation for advanced execution modes.

Variogram Tuning & Stationarity Constraints

The variogram defines how spatial correlation decays with distance. Three parameters control the model:

• Nugget: Micro-scale variation or measurement error. Yield monitors typically exhibit 5–15% nugget due to GPS drift and combine harvester lag.
• Sill: Total variance where spatial correlation plateaus. Should approximate the sample variance of your yield column.
• Range: Distance at which the sill is reached. Represents the effective influence radius of a single yield observation.

Automated fitting (nlags=12) works for moderately dense fields but fails on sparse data. When points are >200m apart, manually constrain the range to 1.5× your maximum sampling interval. If the experimental variogram shows directional anisotropy (e.g., correlation stretches along planting rows), switch to an anisotropic model or apply a directional trend surface before kriging.

Validation & Downstream Integration

Never deploy an interpolated raster without cross-validation. Use leave-one-out or k-fold validation to compute RMSE and mean absolute error. High variance bands (ss output) flag areas where predictions are unreliable—typically field edges, headlands, or zones with >150m gaps between passes. Mask these regions before generating agronomic prescriptions.

The exported GeoTIFF aligns directly with standard farm management software. Clip the raster to your field boundary using rasterio.mask or gdalwarp, then resample to your controller’s native resolution. This raster serves as the foundational layer for Yield Mapping & Variable Rate Prescription Generation, enabling zone delineation, seed rate optimization, and fertilizer application maps.