| 07 Sep 2026
Novel analogue-based and geostatistical approaches for space-time prediction of environmental variables
Abstract. In many environmental applications, it is important to obtain accurate and coherent reconstructions of environmental maps. These can be for example spatial representations of hydrological variables or satellite-based remote sensing products. To do this, analogue-based methods provide a fast and interpretable approach that is based on replicating patterns coming from historical observations and predictor similarity. However, their classical weighted-average aggregation tends to smooth spatial variability and attenuate extremes. This study evaluates whether analogue-based reconstruction of MODIS evapotranspiration (ET) over the Ebro watershed can be improved through local analogue selection and stochastic pattern-based aggregation. Several strategies are compared, including domain-wise and tile-wise analogue selection, inverse-distance weighted averaging, and two Multiple-Point Statistics simulation techniques, chessQS and a new method named Anchor Sampling. Weighted averaging provides the best pixel-wise accuracy, image-structure agreement, and computational efficiency, while tile-wise analogue selection yields only marginal improvements over domain-wise selection. Anchor Sampling offers the most balanced stochastic option, improving variogram agreement, timestep water-balance error, and tail-value statistics while remaining closer to the deterministic baseline than chessQS. In contrast, chessQS increases spatial flexibility but reduces reconstruction accuracy and image-structure agreement in the present application. The results indicate that stochastic aggregation can help preserve aspects of spatial variability and distributions, but that simple analogue averaging remains a strong baseline for ET map reconstruction, unless the realism of the spatial structure or uncertainty representation are specifically required.
General comments
The authors present a fairly objective intercomparison of three different analogue-based approaches to reconstructing MODIS evapotranspiration maps in the Ebro watershed of Spain: inverse-distance weighted averaging, a stochastic QuickSampling strategy called chessQS, and a novel stochastic method called Anchor Sampling. The authors conclude that classical inverse-distance weighted averaging remains a good practical choice to balance model performance and computational efficiency, while the stochastic methods may be most useful for specific scenarios, e.g., Anchor Sampling captures tail statistics best, while chessQS may be a good choice if spatial variables like land cover and land use change over time. Overall, the authors’ presentation is detailed and clear, however, there are some aspects of the presentation I feel could use improvement.
If computational resources are limited, I do not ask that the authors implement tile-wise analogue selection for stochastic scenarios, or to generate ensembles of realizations, but I do ask that the authors provide more context and stronger justification for their decisions with respect to these points. I also ask that the authors address a few more minor points below.
I would therefore recommend this article for publication subject to minor revisions.
Specific comments
Line 121: Define “spatial averaging”.
Lines 136-137: How are you “aggregating the hourly ERA5-Land fields”?
Lines 160-163: How is the antecedent period included? Is it added in as additional predictor fields, but grouped by variable? Is it averaged over the period? Please elaborate.
Figure 4: What is the difference between the green and pink panels? Would it be possible to label tiles and overlaps? This figure was a little difficult to digest.
Lines 245-246: Is the averaging in overlaps simple averaging, or is there a different weighting strategy?
Line 268: If I understand correctly, the training images for the chessQS scenarios include a similarity covariate which is encoded as the analogue distance to zero, to cause training to favor smaller distances? What is the rationale for this? To help keep chessQS from “moving” too far from the observed spatial patterns?
Table 3: What are the units on these metrics? Are these differences significant?
Line 387: Are “01.01” etc. dates? Please make this more clear.
Lines 398-399: How were the “pragmatic conditioning parameters” chosen?