We estimate annual runoff by using a Bayesian geostatistical model for interpolation of hydrological data of different spatial support: streamflow observations from catchments (areal data), and precipitation and evaporation data (point data). The model contains one climatic spatial effect that is common for all years under study, and 1 year specific spatial effect. Hence, the framework enables a quantification of the spatial variability caused by long-term weather patterns and processes. This can contribute to a better understanding of biases and uncertainties in environmental modelling. The suggested model is evaluated by predicting annual runoff for catchments around Voss in Norway and through a simulation study. We find that on average we benefit from combining point and areal data compared to using only one of the data types, and that the interaction between nested areal data and point data gives a spatial model that takes us beyond smoothing. Another finding is that when climatic effects dominate over annual effects, systematic under- and overestimation of runoff can be expected over time. However, a dominating climatic spatial effect also implies that short records of runoff from an otherwise ungauged catchment can lead to large improvements in the predictive performance.

中文翻译：

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结合点和面观测的两场地质统计模型——以沃斯地区年度径流预测为例

我们通过使用贝叶斯地质统计模型对不同空间支持的水文数据进行插值来估计年径流：来自集水区的流量观测（区域数据）以及降水和蒸发数据（点数据）。该模型包含一个对所有研究年份通用的气候空间效应和 1 年特定空间效应。因此，该框架能够量化由长期天气模式和过程引起的空间变化。这有助于更好地理解环境建模中的偏差和不确定性。建议的模型是通过预测挪威 Voss 周围集水区的年度径流并通过模拟研究来评估的。我们发现，与仅使用一种数据类型相比，平均而言，我们从结合点数据和区域数据中受益，并且嵌套区域数据和点数据之间的相互作用提供了一个空间模型，使我们超越了平滑。另一个发现是，当气候影响超过年度影响时，随着时间的推移，可以预期径流的系统性低估和高估。然而，占主导地位的气候空间效应也意味着来自未经测量的集水区的短期径流记录可以导致预测性能的大幅提高。