Short observation series and geostatistical methods improve Norwegian mean annual runoff maps. 

By Thea Roksvåg and Ingelin Steinsland

Norwegian Computing Center and NTNU

The mean annual runoff is a key variable in Hydrology. Runoff can be defined as the part of precipitation that does not evaporate, but travels over the land surface or within the soil before it reaches a river.  Although runoff is of interest for a variety of reasons, most areas in the world lack runoff measurements, and runoff must be estimated. This can be done by using statistical methods. 

Thea Roksvåg has written her Ph.d thesis at the department of mathematical sciences at NTNU, under the supervision of Professor Ingelin Steinsland (NTNU) and of Senior Researcher Kolbjørn Engeland from the Norwegian water resources and Energy Directorate (NVE). Thea developed geostatistical interpolation models for improved estimation of annual runoff. She successfully defended her thesis in 2020. Two years later, in December 2022, NVE launched a new, gridded mean annual runoff product for Norway, the first since 2002 (Beldring et al.,2022). Here, NVE used Thea’s interpolation methods to postprocess, or correct, runoff estimates from the hydrological model WASMOD (Xu et al., 2002). 

Fig 1: Gridded mean annual runoff maps (mm/year) produced by using the WASMOD model alone (a) and when correcting WASMOD by geostatistical interpolation (b). The figures are taken from Beldring et al.,(2022).

In Norway around 90 % of the electrical energy produced comes from hydroelectricity (Energifakta,2022), and runoff estimates, and forecasts are needed to plan the hydropower production. Estimates of mean annual runoff give information about the long-term water availability across the country.  This can be useful when choosing potential locations for new hydropower plants or to estimate the expected amount of electricity available. Furthermore, it is important to estimate runoff and runoff extremes for flood security reasons. 

Thea Roksvåg’s work is based on the idea of exploiting short records of runoff (Vogel and Stedinger, 1985; Blöschl et al., 2013). For hydrologists it is often of interest to estimate the long-term behavior of runoff, for example the mean annual runoff is based on 30 years. However, in some catchments there only exist 1, 3, 10 or 28 years of observations. These data records are what hydrologists refer to as short records. 

The Norwegian water resources and Energy Directorate (NVE) is responsible for making gridded mean annual runoff maps with 1 x 1 km resolution for Norway. In the previous version of the map, launched in 2002, data from rivers with short records were omitted from the analysis (Beldring et al., 2002).  The reason was that short records were considered too uncertain and/or too complicated to include in an analysis with the existing methods for runoff interpolation. However, omitting these represented a reduction in the number of observation locations of more than 50 % in Norway.

Motivated by the challenge of exploiting short records, Thea and her collaborators developed a Bayesian spatial model for annual runoff that models several years of runoff simultaneously with two spatial fields: One that represents the long-term average spatial variability of runoff, and one that represents year-specific spatial variability. The model made it possible to quantify how much of the runoff that can be explained by repeated geographical runoff patterns and how much that is due to year-specific effects. This could next be used to fill in missing runoff data by exploiting spatial correlations. Prediction experiments with Norwegian runoff data, showed that with the new model, only one year of runoff data from a river could lead to considerable improvements in the 30-year mean annual runoff estimates for that river’s drainage area (Roksvåg et al.,2020).

In addition to the study of the two-field model for exploiting short records, the thesis explores methods for combining different data sources in a spatial model (Roksvåg et al.,2022). A main goal was to develop models that were computationally feasible for operational use.  

Figure 1a) shows the mean annual runoff map NVE obtained when using the WASMOD model alone, while Figure 1b) shows the map after performing geostatistical correction with short (and long) records. The scatter plots in Figure 2 compare the runoff estimates from the gridded maps to the actually observed mean annual runoff for river’s where there are runoff measurements available. We see how the geostatistical correction improves the accuracy of the map. The geostatistical correction also improves the map in areas where there are no runoff measurements (Beldring et al.,2022).

Fig 2: Comparing the observed mean annual runoff (x-axis) to the estimated mean annual runoff in the maps (y-axis) for drainage areas with runoff measurements. Results are shown for the map produced by WASMOD alone (a) and for the map that was corrected with geostatistical interpolation (b) with unit mm/year. The figures are taken from Beldring et al. (2022).
Fig 3: Average annual runoff for (a) 1961-1990 and (b) 1991-2020. Both maps are based on the new methods. Figure (c) shows the difference between the two maps, where blue and green indicates that the runoff has increased, and yellow and red indicates that the runoff has decreased. The figures are taken from Beldring et al.(2022).

Ingelin Steinsland is a professor at the Department of Mathematical Sciences and the Vice Dean of research at the Faculty of Information Technology and Electrical Engineering. She has a MSc in Industrial Mathematics and a PhD in Statistics from NTNU.



Thea Roksvåg is a researcher at the Norwegian Computing Center in Oslo. She has a MSc in Industrial Mathematics and a PhD in Statistics from NTNU. Her expertise is in applications of statistics to weather and climate.



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