Research papersSignal to noise ratio in water balance maps with different resolution

- To find the best resolution of annual water balance maps for a correct balance between the signal in the observations of precipitation, actual evapotranspiration and runoff across a larger drainage basin and the error in estimates for grid cells in the map to avoid giving a false impression of accuracy, an approach based a signal to noise ratio is proposed, which allows finding the optimal resolution for which the signal in the map is maximized.
- Stochastic interpolation methods were applied to estimate grid maps of long-term mean values as well as estimation variances of the three water balance components in a range of scales from 5 × 5 km to 200 × 200 km grid cells.
- Interpolation algorithms using covariances of long-term means of data with different spatial support were developed. The identified optimal resolutions by the signal to noise ratio turned out to be very different for precipitation, actual evapotranspiration, and runoff, respectively, which are directly linked to measures of the observation network densities.
- The magnitude of the signal to noise ratio can be seen as a direct indication of the reliability of the map, which can be considered as satisfactory only for precipitation for the available data used in the present study. Critical factors for this magnitude are parameters characterizing the spatial covariance in data and the network density.

What is the best resolution of annual water balance maps for a correct balance between the basic spatial signal in the observations of precipitation, actual evapotranspiration and runoff across a larger drainage basin and the error in estimates for grid cells in the map to avoid giving a false impression of accuracy? To answer this question an approach based a signal to noise ratio is proposed, which allows finding the optimal resolution maximizing the signal in the map. The approach is demonstrated on gauge data in the Huai River Basin, China. Stochastic interpolation methods were applied to create grid maps of long-term mean values, as well as for estimating variances of the three water balance components in a range of scales from 5 × 5 km to 200 × 200 km2 grid cells. Interpolation algorithms using covariances of long-term means of data with different spatial support were developed. The identified optimal resolutions by the signal to noise ratio appeared to be very different - 10 × 10, 50 × 50, and 30 × 30 km2 for precipitation, actual evapotranspiration, and runoff, respectively. These values are directly linked to the observation network densities. The magnitude of the signal to noise ratio shows similar strong differences with values 34, 3.7, and 5.4, respectively. It gives a direct indication of the reliability of the map, which can be considered as satisfactory only for precipitation for the data available for the present study. The critical factors for this magnitude are parameters characterising the spatial covariance in data and the network density.