Abstract The intent of this paper is to encourage improved numerical implementation of land models. Our contributions in this paper are two-fold. First, we present a unified framework to formulate and implement land model equations. We separate the representation of physical processes from their numerical solution, enabling the use of established robust numerical methods to solve the model equations. Second, we introduce a set of synthetic test cases (the laugh tests) to evaluate the numerical implementation of land models. The test cases include storage and transmission of water in soils, lateral sub-surface flow, coupled hydrological and thermodynamic processes in snow, and cryosuction processes in soil. We consider synthetic test cases as “laugh tests” for land models because they provide the most rudimentary test of model capabilities. The laugh tests presented in this paper are all solved with the Structure for Unifying Multiple Modeling Alternatives model (SUMMA) implemented using the SUite of Nonlinear and DIfferential/Algebraic equation Solvers (SUNDIALS). The numerical simulations from SUMMA/SUNDIALS are compared against (1) solutions to the synthetic test cases from other models documented in the peer-reviewed literature; (2) analytical solutions; and (3) observations made in laboratory experiments. In all cases, the numerical simulations are similar to the benchmarks, building confidence in the numerical model implementation. We posit that some land models may have difficulty in solving these benchmark problems. Dedicating more effort to solving synthetic test cases is critical in order to build confidence in the numerical implementation of land models.

Abstract Stations are an important source of meteorological data, but often suffer from missing values and short observation periods. Gap filling is widely used to generate serially complete datasets (SCDs), which are subsequently used to produce gridded meteorological estimates. However, the value of SCDs in spatial interpolation is scarcely studied. Based on our recent efforts to develop a SCD over North America (SCDNA), we explore the extent to which gap filling improves gridded precipitation and temperature estimates. We address two specific questions: (1) Can SCDNA improve the statistical accuracy of gridded estimates in North America? (2) Can SCDNA improve estimates of trends on gridded data? In addressing these questions, we also evaluate the extent to which results depend on the spatial density of the station network and the spatial interpolation methods used. Results show that the improvement in statistical interpolation due to gap filling is more obvious for precipitation, followed by minimum temperature and maximum temperature. The improvement is larger when the station network is sparse and when simpler interpolation methods are used. SCDs can also notably reduce the uncertainties in spatial interpolation. Our evaluation across North America from 1979 to 2018 demonstrates that SCDs improve the accuracy of interpolated estimates for most stations and days. SCDNA-based interpolation also obtains better trend estimation than observation-based interpolation. This occurs because stations used for interpolation could change during a specific period, causing changepoints in interpolated temperature estimates and affect the long-term trends of observation-based interpolation, which can be avoided using SCDNA. Overall, SCDs improve the performance of gridded precipitation and temperature estimates.

Abstract In this study, two sets of precipitation estimates based on the regional Weather Research and Forecasting model (WRF) –the high Asia refined analysis (HAR) and outputs with a 9 km resolution from WRF (WRF-9km) are evaluated at both basin and point scales, and their potential hydrological utilities are investigated by driving the Variable Infiltration Capacity (VIC) large-scale land surface hydrological model in seven Third Pole (TP) basins. The regional climate model (RCM) tends to overestimate the gauge-based estimates by 20–95% in annual means among the selected basins. Relative to the gauge observations, the RCM precipitation estimates can accurately detect daily precipitation events of varying intensities (with absolute bias < 3 mm). The WRF-9km exhibits a high potential for hydrological application in the monsoon-dominated basins in the southeastern TP (with NSE of 0.7–0.9 and bias of -11% to 3%), while the HAR performs well in the upper Indus (UI) and upper Brahmaputra (UB) basins (with NSE of 0.6 and bias of -15% to -9%). Both the RCM precipitation estimates can accurately capture the magnitudes of low and moderate daily streamflow, but show limited capabilities in flood prediction in most of the TP basins. This study provides a comprehensive evaluation of the strength and limitation of RCMs precipitation in hydrological modeling in the TP with complex terrains and sparse gauge observations.

Abstract Obtaining reliable water balance estimates remains a major challenge in Canada for large regions with scarce in situ measurements. Various remote sensing products can be used to complement observation-based datasets and provide an estimate of the water balance at river basin or regional scales. This study provides an assessment of the water balance using combinations of various remote sensing and data assimilation-based products and quantifies the non-closure errors for river basins across Canada, ranging from 90,900 to 1,679,100 km 2 , for the period from 2002 to 2015. A water balance equation combines the following to estimate the monthly water balance closure: multiple sources of data for each water budget component, including two precipitation products - the global product WATCH Forcing Data ERA-Interim (WFDEI), and the Canadian Precipitation Analysis (CaPA); two evapotranspiration products - MODIS, and Global Land-surface Evaporation: the Amsterdam Methodology (GLEAM); one source of water storage data - GRACE from three different centers; and observed discharge data from hydrometric stations (HYDAT). The non-closure error is attributed to the different data products using a constrained Kalman filter. Results show that the combination of CaPA, GLEAM, and the JPL mascon GRACE product tended to outperform other combinations across Canadian river basins. Overall, the error attributions of precipitation, evapotranspiration, water storage change, and runoff were 36.7, 33.2, 17.8, and 12.2 percent, which corresponded to 8.1, 7.9, 4.2, and 1.4 mm month -1 , respectively. In particular, non-closure error from precipitation dominated in Western Canada, whereas that from evapotranspiration contributed most in the Mackenzie River basin.