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Predictions of hydrologic system response to natural and anthropogenic forcing are highly uncertain due to the heterogeneity of the land surface and subsurface. Landscape heterogeneity results in spatiotemporal variability of hydrological states and fluxes, scale‐dependent flow and transport properties, and incomplete process understanding. Recent community activities, such as Prediction in Ungauged Basins of International Association of Hydrological Sciences, have recognized the impasse current catchment hydrology is facing and have called for a focused research agenda toward new hydrological theory at the watershed scale. This new hydrological theory should recognize the dominant control of landscape heterogeneity on hydrological processes, should explore novel ways to account for its effect at the watershed scale, and should build on an interdisciplinary understanding of how feedback mechanisms between hydrology, biogeochemistry, pedology, geomorphology, and ecology affect catchment evolution and functioning.

Abstract. Commonly used bias correction methods such as quantile mapping (QM) assume the function of error correction values between modelled and observed distributions are stationary or time-invariant. This article finds that this function of the error correction values cannot be assumed to be stationary. As a result, QM lacks justification to inflate/deflate various moments of the climate change signal. Previous adaptations of QM, most notably quantile delta mapping (QDM), have been developed that do not rely on this assumption of stationarity. Here, we outline a methodology called scaled distribution mapping (SDM), which is conceptually similar to QDM, but more explicitly accounts for the frequency of rain days and the likelihood of individual events. The SDM method is found to outperform QM, QDM and detrended QM in its ability to better preserve raw climate model projected changes to meteorological variables such as temperature and precipitation.

Forecast skill of numerical weather prediction (NWP) models for precipitation accumulations over California is rather limited at subseasonal time scales, and the low signal-to-noise ratio makes it challenging to extract information that provides reliable probabilistic forecasts. A statistical postprocessing framework is proposed that uses an artificial neural network (ANN) to establish relationships between NWP ensemble forecast and gridded observed 7-day precipitation accumulations, and to model the increase or decrease of the probabilities for different precipitation categories relative to their climatological frequencies. Adding predictors with geographic information and location-specific normalization of forecast information permits the use of a single ANN for the entire forecast domain and thus reduces the risk of overfitting. In addition, a convolutional neural network (CNN) framework is proposed that extends the basic ANN and takes images of large-scale predictors as inputs that inform local increase or decrease of precipitation probabilities relative to climatology. Both methods are demonstrated with ECMWF ensemble reforecasts over California for lead times up to 4 weeks. They compare favorably with a state-of-the-art postprocessing technique developed for medium-range ensemble precipitation forecasts, and their forecast skill relative to climatology is positive everywhere within the domain. The magnitude of skill, however, is low for week-3 and week-4, and suggests that additional sources of predictability need to be explored.