Space-Time Kriging
Also known as: spatiotemporal kriging, ST-kriging, space-time geostatistical interpolation, kriging in space-time
Space-Time Kriging is a geostatistical interpolation method that predicts an unknown variable at any location and time by borrowing strength from nearby observations in both space and time simultaneously. It models the joint spatial-temporal covariance structure through a space-time variogram, then uses optimal linear weights to produce predictions with quantified uncertainty.
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When to use it
Use Space-Time Kriging when you have spatially distributed measurements collected at multiple time points and need to interpolate values at unsampled locations or times — for example, filling gaps in air quality networks, climate station records, or soil-monitoring grids. It is most valuable when the data exhibit clear spatial autocorrelation and temporal autocorrelation simultaneously. It is not appropriate when observations are purely cross-sectional (a single snapshot without temporal replication), when the number of monitoring stations is very small (fewer than ~15-20), when the variable is binary or count-based, or when the space-time covariance structure cannot be adequately modelled (e.g., highly irregular or nonstationary processes without detrending).
Strengths & limitations
- Jointly exploits spatial and temporal correlations, using more information than separate spatial or temporal interpolation.
- Provides not just predictions but also kriging variances — spatially and temporally varying uncertainty estimates.
- Flexible covariance family choices (separable, nonseparable, product-sum) let the analyst match the true space-time dependence structure.
- Theoretically optimal (minimum mean squared error) among all linear unbiased interpolators under the assumed covariance model.
- Handles irregular sampling grids in both space and time without requiring a regular lattice.
- Computational cost scales as O(n^3) with the number of observations; large datasets (thousands of space-time points) require approximations or sparse covariance methods.
- Assumes second-order stationarity (constant mean and covariance depending only on lag); non-stationarity must be removed by detrending or accounted for with extensions like universal space-time kriging.
- Fitting a reliable space-time variogram requires adequate coverage of both short and long spatial and temporal lags — sparse or irregular sampling may yield a poorly identified covariance model.
- Predictions can be unreliable far outside the sampled time range (extrapolation) even if spatial coverage is good.
Frequently asked
What is the difference between separable and nonseparable space-time covariance?
A separable covariance factors as C(h,u) = C_S(h) * C_T(u): the spatial and temporal components are independent. Nonseparable models add interaction terms, allowing, for example, variables that are more spatially smooth at short time lags than long ones. Nonseparable models are more flexible but need more data to fit reliably.
How many observations do I need for Space-Time Kriging?
There is no fixed rule, but you need enough space-time pairs at varying lags to estimate the variogram reliably. Practically, at least 15-20 spatial stations with 5 or more repeated measurements is a rough lower bound. Very sparse datasets produce poorly identified covariance models and unreliable predictions.
Can Space-Time Kriging handle non-stationary data?
Standard space-time kriging assumes second-order stationarity. Non-stationarity (trends in mean or variance) must be removed first — e.g., subtract a regression-based spatio-temporal trend — before fitting the variogram. Extensions such as universal space-time kriging incorporate a deterministic trend component directly.
How do I validate a space-time kriging model?
Use leave-one-out cross-validation (or block cross-validation to avoid leakage): withhold each observation in turn, predict it from the rest, and compute RMSE and mean standardised error. A well-calibrated model yields standardised errors with mean near 0 and variance near 1.
What software implements Space-Time Kriging?
The R package gstat provides space-time variogram fitting and kriging via the STFDF/STSDF classes. The spacetime and FRK packages offer further options including basis-function approximations for large datasets. Python users can use PyKrige with space-time extensions or the pykrige-st fork.
Sources
- Cressie, N., & Huang, H.-C. (1999). Classes of nonseparable, spatio-temporal stationary covariance functions. Journal of the American Statistical Association, 94(448), 1330-1340. DOI: 10.1080/01621459.1999.10473885 ↗
- Kyriakidis, P. C., & Journel, A. G. (1999). Geostatistical space-time models: A review. Mathematical Geology, 31(6), 651-684. DOI: 10.1023/A:1007528426688 ↗
How to cite this page
ScholarGate. (2026, June 3). Space-Time Kriging. ScholarGate. https://scholargate.app/en/spatial-analysis/space-time-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.
- Co-krigingSpatial analysis↔ compare
- Ordinary KrigingSpatial analysis↔ compare
- Space-Time Spatial AutocorrelationSpatial analysis↔ compare
- Universal KrigingSpatial analysis↔ compare