03 May 2021
03 May 2021
Status: a revised version of this preprint is currently under review for the journal HESS.

A geostatistical spatially varying coefficient model for mean annual runoff that incorporates process-based simulations and short records

Thea Roksvåg1,2, Ingelin Steinsland1, and Kolbjørn Engeland3 Thea Roksvåg et al.
  • 1Norwegian University of Science and Technology, NTNU, Høgskoleringen 1, 7491 Trondheim, Norway
  • 2Norwegian Computing Center, NR, Gaustadalléen 23A, 0373 Oslo, Norway
  • 3The Norwegian Water Resources and Energy Directorate, NVE, Middelthuns gate 29, 0368 Oslo, Norway

Abstract. We present a Bayesian geostatistical model for mean annual runoff that incorporates simulations from a process-based hydrological model by treating the simulations as a covariate in the statistical model. The regression coefficient of the covariate is modeled as a spatial field such that the relationship between the covariate (simulations from a hydrological model) and the response variable (observed mean annual runoff) is allowed to vary within the study area. Hence, it is a spatially varying coefficient. A preprocessing step for including short records in the modeling is also suggested and we obtain a model that can exploit several data sources by using state of the art statistical methods.

The geostatistical model is evaluated by predicting mean annual runoff for 1981–2010 for 127 catchments in Norway based on observations from 411 catchments. Simulations from the process-based HBV model on a 1 km × 1 km grid are used as input. We found that on average the proposed approach outperformed a purely process-based approach (HBV) when predicting runoff for ungauged and partially gauged catchments: The reduction in RMSE compared to the HBV model was 20 % for ungauged catchments and 58 % for partially gauged catchments, where the latter is due to the preprocessing step. For ungauged catchments the proposed framework also outperformed a purely geostatistical method with a 10 % reduction in RMSE compared to the geostatistical method. For partially gauged catchments however, purely geostatistical methods performed equally well or slightly better than the proposed combination approach. It is not surprising that purely geostatistical methods perform well in areas where we have data. In general, we expect the proposed approach to outperform geostatistics in areas where the data availability is low to moderate.

Thea Roksvåg et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-8', Anonymous Referee #1, 24 Jun 2021
    • AC1: 'Reply on RC1', Thea Roksvåg, 12 Jul 2021
  • RC2: 'Comment on hess-2021-8', Anonymous Referee #2, 24 Jun 2021
    • AC2: 'Reply on RC2', Thea Roksvåg, 12 Jul 2021

Thea Roksvåg et al.

Thea Roksvåg et al.


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Short summary
The goal of this work was to make a map of the mean annual runoff of Norway based on a 30 year period. We first simulated runoff by using a process-based model that models the relationship between runoff, precipitation, temperature and land use. Next, we corrected the map based on runoff observations from rivers by using a statistical method. We were also able to use data from rivers that only had a few annual observations. We find that the statistical correction improves the runoff estimates.