Downscaling runoff products using areal interpolation: A combined pycnophylactic-dasymetric method

Hydrological models are commonly forced with variables describing climate. These variables are often obtained from climate models, requiring processing via interpolation or downscaling in order to be useful for the hydrological modelling study. Outputs from climate- A s well as hydrological-models are generally expressed as spatially explicit fields, but the results from hydrological models are rarely interpolated or downscaled. There can be many reasons for this. For instance, the existing model output may be of incompatible spatial units (raster, when vector needed, or vice versa), or of a different scale (regional, where local scale is needed). Runoff generation is a local process which is determined by the influx of water, landuse, vegetation and soil characteristics, and there have been many applications of its interpolation to watersheds, river lines or as continuous fields. However, most of the methods employed in runoff interpolation are statistical and do not account for process characteristics in runoff generation in the interpolation step. Here we present a novel spatial interpolation method for the purpose of downscaling coarse resolution runoff products based on areal interpolation. Areal interpolation is a process where a variable from a source zone is reallocated to overlapping target zones. We combine two advanced methods: Dasymetric Mapping (DM), which is simple Area weighted Interpolation (AI) informed by an ancillary variable, and Pycnophylactic Interpolation (PP), which is designed to refine the spatial distribution of a variable within the source zone. Each of these methods preserve mass balance-the volume of runoff from source zone is preserved in the target zones. Our methodology can address the Modifiable Area Unit Problem (MAUP)- A statistical bias caused by the sensitivity of analytical results of spatial data to levels of aggregation (the scale effect), as well as the arbitrary sizes, shapes, and arrangements of zones (the zoning effect). Addressing MAUP enhances usability of existing model results for runoff estimation because the zoning can be modified to fit the needs of a new analysis. The method is also able to take into account the spatial distribution of characteristics which govern runoff generation in the interpolation step. To test the methodology, we downscale a coarse global runoff product, LORA (Linear Optimal Runoff Aggregate), on to 126 Australian catchments with natural flow regimes, and compare how AI, DM, PP and the combined PP-DM fare against streamflow records. A recently developed topographical index, DUNE (Dissipation Per Unit Length), which is able to distinguish topographies with different runoff regimes, is used as the ancillary variable in DM and PP-DM. We assume that runoff is highly correlated with precipitation and we assume it can be interpolated with a smooth function. We also assume that topography can inform us about the actual distribution of runoff generation within a source zone (the spatial unit in a runoff product). We find that the simple AI method is more efficient in replicating the runoff profile in arid catchments where potential evapotranspiration is higher than precipitation. However, as precipitation increases and aridity is reduced, DM and PP-DM prove more efficient in replicating the recorded runoff. Using DUNE as the ancillary variable also results in higher performance in catchments with variable topography and performs worse in less variable terrain. In catchments with a high range of slopes, DM and PP-DM utilizing DUNE are consistently better than AI or PP, which do not utilize DUNE. Additionally, we find that in wet catchments which are located entirely within a single source zone of runoff, the performance is higher using DM, PP, and PP-DM than with the simple AI. In catchments which are covered by multiple source zones there is no clear benefit in using the more advanced areal interpolation methods over AI. Our results show that the method is able capture the spatial variability of runoff generation, but this requires careful selection of the ancillary variable or a combination of ancillary variables. It is also evident from the results that arid and wet catchments require a different approach in runoff downscaling. Further investigation with a larger sample is needed to fully understand the properties of the downscaling methods.