Abstract. In this article, we present a Bayesian geostatistical framework that is particularly suitable for interpolation of hydrological data when the available dataset is sparse and includes both long and short records of runoff. A key feature of the proposed framework is that several years of runoff are modelled simultaneously with two spatial fields: one that is common for all years under study that represents the runoff generation due to long-term (climatic) conditions and one that is year-specific. The climatic spatial field captures how short records of runoff from partially gauged catchments vary relative to longer time series from other catchments, and transfers this information across years. To make the Bayesian model computationally feasible and fast, we use integrated nested Laplace approximations (INLAs) and the stochastic partial differential equation (SPDE) approach to spatial modelling. The geostatistical framework is demonstrated by filling in missing values of annual runoff and by predicting mean annual runoff for around 200 catchments in Norway. The predictive performance is compared to top-kriging (interpolation method) and simple linear regression (record augmentation method). The results show that if the runoff is driven by processes that are repeated over time (e.g. orographic precipitation patterns), the value of including short records in the suggested model is large. For partially gauged catchments the suggested framework performs better than comparable methods, and one annual observation from the target catchment can lead to a 50 % reduction in root mean squared error (RMSE) compared to when no observations are available from the target catchment. We also find that short records safely can be included in the framework regardless of the spatial characteristics of the underlying climate, and down to record lengths of 1 year.

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Agricultural food production and natural ecological systems depend on a range of seasonal climate indicators that describe seasonal patterns in climatological conditions. This paper proposes a probabilistic forecasting framework for predicting the end of the freeze-free season, or the time to a mean daily near-surface air temperature below 0 • C (here referred to as hard freeze). The forecasting framework is based on the multi-model seasonal forecast ensemble provided by the Copernicus Climate Data Store and uses techniques from survival analysis for time-to-event data. The original mean daily temperature forecasts are statistically post-processed with a mean and variance correction of each model system before the time-to-event forecast is constructed. In a case study for a region in Fennoscandia covering Norway for the period 1993-2020, the proposed forecasts are found to outperform a climatology forecast from an observation-based data product at locations where the average predicted time to hard freeze is less than 40 days after the initialization date of the forecast on October 1.

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<p>In the agricultural sector there is a high interest for forecasts that predict relevant agroclimatic indicators related to heat accumulation and frost characteristics. The forecasts can simplify agricultural decisions related to planting and harvest timing. Motivated by this, we propose a probabilistic forecasting framework for predicting the end of the freeze-free season, or the time to a mean daily near-surface air temperature below 0 <sup>°</sup>C (here referred to as hard freeze). The forecasts are constructed based on a multi-model seasonal temperature forecast ensemble provided by the Copernicus Climate Data Store. The raw temperature forecast is statistically post-processed through a mean and variance correction. The resulting ensemble is next used as input to a survival analysis model. Survival analysis is a broad statistical field that is commonly used in the field of biostatistics, but rarely used in meteorology.</p><p>The forecasting framework is evaluated by predicting the time to hard freeze from October 1 for 1993-2020 for a region in Fennoscandia that covers Norway and parts of Sweden, Finland and Russia. We find that the proposed forecast outperforms a climatology forecast from an observation-based data product at locations where the average predicted time to hard freeze is less than 40 days after the initialization date.</p><p>Our work also forms an entry point showing how survival models can be used in general to construct seasonal forecasts for other meteorological events, e.g. the onset of the rainy season or the time to the next drought.</p>