Space-Time Ordinary Kriging
Also known as: STOK, spatio-temporal ordinary kriging, ordinary space-time kriging, ST-OK
Space-Time Ordinary Kriging (STOK) is a geostatistical interpolation method that predicts a spatially and temporally varying phenomenon at unsampled space-time locations by combining the ordinary kriging assumption of an unknown, locally constant mean with a joint space-time covariance (or variogram) structure. It produces optimal, unbiased predictions along with associated estimation uncertainty.
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When to use it
Use Space-Time Ordinary Kriging when you have georeferenced, time-stamped observations of a continuous variable and need to interpolate values at unobserved space-time locations, especially when the global mean is unknown or not constant across the study region. It is appropriate when the variable is second-order stationary (constant mean and space-time covariance depending only on separation), when spatial and temporal autocorrelation are both present, and when uncertainty quantification (kriging variance) is required alongside the estimates. Do not use it when the mean varies systematically with coordinates or covariates (use space-time universal kriging instead), when the data are strongly non-stationary across large extents, when the variable is categorical or binary, or when only spatial structure exists with no meaningful temporal correlation.
Strengths & limitations
- Produces best linear unbiased predictions (BLUP) under second-order stationarity — optimal in the mean-squared-error sense.
- Jointly models spatial and temporal autocorrelation through a single space-time variogram, capturing the interplay between the two dimensions.
- Delivers a kriging variance surface alongside predictions, giving principled, location-specific uncertainty quantification.
- Requires no assumed functional form for the mean surface — the constant-mean assumption is automatically estimated from local neighbours.
- Well-supported by mature open-source implementations (e.g., gstat in R) and peer-reviewed theory.
- Assumes second-order stationarity (constant mean and covariance); violated by trends or non-stationary variance, leading to biased predictions.
- Fitting a valid joint space-time variogram model is technically demanding; mis-specification propagates into prediction errors.
- Computational cost scales cubically with the number of space-time data points in the neighbourhood; large datasets require neighbourhood truncation.
- Space-time neighbourhood definition (search radius in both space and time) strongly influences results and requires careful tuning.
- Does not incorporate auxiliary covariates; if informative covariates are available, space-time regression-kriging or co-kriging is preferable.
Frequently asked
What is the difference between Space-Time Ordinary Kriging and Space-Time Universal Kriging?
Ordinary kriging assumes an unknown but constant (stationary) mean across the space-time domain and estimates it implicitly via the unbiasedness constraint. Universal kriging allows the mean to vary as a known function of spatial coordinates or time, making it more flexible but requiring specification of a drift model. When the mean is clearly non-stationary (e.g., a temperature gradient with latitude), universal kriging is preferred.
How do I choose a space-time variogram model?
Common choices are the separable model (product of a purely spatial and purely temporal variogram), the product-sum model (adds a joint component), and the metric model (uses a rescaled Euclidean distance combining space and time). Fit each to the empirical variogram and compare residual sums of squares. The product-sum model often captures non-separable dependence better than the separable model.
Can Space-Time Ordinary Kriging handle irregular temporal sampling?
Yes. Because kriging is a point-wise method that uses the variogram evaluated at any arbitrary space-time separation, it naturally handles irregular sampling in both space and time without requiring a regular grid of observations.
How large a dataset can Space-Time Ordinary Kriging handle?
Direct inversion of the full covariance matrix is O(n^3), so it becomes impractical beyond a few thousand observations. In practice, a local search neighbourhood (e.g., the 20-50 nearest space-time neighbours) is used, which reduces cost and also enforces local stationarity. For very large datasets, covariance tapering or fixed-rank approximations are alternatives.
Does the method account for measurement errors?
Adding a nugget effect to the variogram model absorbs both short-range variability and measurement noise. The kriging predictor then does not honour the data exactly (no exact interpolation), which can be beneficial when observations contain noise.
Sources
- Kyriakidis, P. C., & Journel, A. G. (1999). Geostatistical space-time models: a review. Mathematical Geology, 31(6), 651-684. DOI: 10.1023/A:1007528426688 ↗
- Gräler, B., Pebesma, E., & Heuvelink, G. (2016). Spatio-temporal interpolation using gstat. The R Journal, 8(1), 204-218. link ↗
How to cite this page
ScholarGate. (2026, June 3). Space-Time Ordinary Kriging. ScholarGate. https://scholargate.app/en/spatial-analysis/space-time-ordinary-kriging
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Ordinary KrigingSpatial analysis↔ compare
- Space-Time KrigingSpatial analysis↔ compare
- Space-Time Spatial AutocorrelationSpatial analysis↔ compare
- Space-Time Universal KrigingSpatial analysis↔ compare