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- Author or Editor: Jinwon Kim x
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Abstract
To understand the influence of the Sierra Nevada on the water cycle in California the authors have analyzed low-level winds and water vapor fluxes upstream of the mountain range in regional climate model simulations. In a low Froude number (Fr) regime, the upstream low-level wind disturbances are characterized by the rapid weakening of the crosswinds and the appearance of a stagnation point over the southwestern foothills. The weakening of the low-level inflow is accompanied by the development of along-ridge winds that take the form of a barrier jet over the western slope of the mountain range. Such upstream wind disturbances are either weak or nonexistent in a high-Fr case. A critical Fr (Fr c ) of 0.35 inferred in this study is within the range of those suggested in previous observational and numerical studies. The depth of the blocked layer estimated from the along-ridge wind profile upstream of the northern Sierra Nevada corresponds to Fr c between 0.3 and 0.45 as well. Associated with these low-level wind disturbances are significant low-level southerly moisture fluxes over the western slope and foothills of the Sierra Nevada in the low-Fr case, which result in significant exports of moisture from the southern Sierra Nevada to the northern region. This along-ridge low-level water vapor transport by blocking-induced barrier jets in a low-Fr condition may result in a strong north–south precipitation gradient over the Sierra Nevada.
Abstract
To understand the influence of the Sierra Nevada on the water cycle in California the authors have analyzed low-level winds and water vapor fluxes upstream of the mountain range in regional climate model simulations. In a low Froude number (Fr) regime, the upstream low-level wind disturbances are characterized by the rapid weakening of the crosswinds and the appearance of a stagnation point over the southwestern foothills. The weakening of the low-level inflow is accompanied by the development of along-ridge winds that take the form of a barrier jet over the western slope of the mountain range. Such upstream wind disturbances are either weak or nonexistent in a high-Fr case. A critical Fr (Fr c ) of 0.35 inferred in this study is within the range of those suggested in previous observational and numerical studies. The depth of the blocked layer estimated from the along-ridge wind profile upstream of the northern Sierra Nevada corresponds to Fr c between 0.3 and 0.45 as well. Associated with these low-level wind disturbances are significant low-level southerly moisture fluxes over the western slope and foothills of the Sierra Nevada in the low-Fr case, which result in significant exports of moisture from the southern Sierra Nevada to the northern region. This along-ridge low-level water vapor transport by blocking-induced barrier jets in a low-Fr condition may result in a strong north–south precipitation gradient over the Sierra Nevada.
Abstract
In preparation for studying the effects of increased CO2 on the hydrologic cycle in the western United States, an 8-yr hindcast was performed using a regional climate model (RCM) driven by the large-scale forcing from the NCEP–NCAR reanalysis. The simulated precipitation characteristics agree well with observations, especially in the winter. The simulated precipitation compares with rain gauge data at similar accuracy as the NCEP reanalysis, but the RCM-generated precipitation is more accurate than the reanalysis data at the scales of individual basins. Important characteristics of the hydrologic cycle of the region, such as seasonal snowfall, frequency of heavy and extreme daily precipitation events, and interannual variations of precipitation associated with the North American monsoon are also well represented in the hindcast. Compared to the Climate Research Unit, University of East Anglia (CRU), analysis, the simulated low-level air temperatures show cold biases except in summer. The temperature biases are difficult to quantify, however, due to suspected warm biases in the CRU data. The RCM overestimates surface insolation and outgoing longwave radiation at the top of the atmosphere (OLR-TOA). The errors in the simulated radiation are smaller over the land than the ocean. Both simulated and observed OLR-TOA suggest strong influence of low-level temperatures on the seasonal variations of OLR-TOA in the region. The results suggest that the RCM employed in this study possesses reasonable skill for studying regional climate change signals in the western United States.
Abstract
In preparation for studying the effects of increased CO2 on the hydrologic cycle in the western United States, an 8-yr hindcast was performed using a regional climate model (RCM) driven by the large-scale forcing from the NCEP–NCAR reanalysis. The simulated precipitation characteristics agree well with observations, especially in the winter. The simulated precipitation compares with rain gauge data at similar accuracy as the NCEP reanalysis, but the RCM-generated precipitation is more accurate than the reanalysis data at the scales of individual basins. Important characteristics of the hydrologic cycle of the region, such as seasonal snowfall, frequency of heavy and extreme daily precipitation events, and interannual variations of precipitation associated with the North American monsoon are also well represented in the hindcast. Compared to the Climate Research Unit, University of East Anglia (CRU), analysis, the simulated low-level air temperatures show cold biases except in summer. The temperature biases are difficult to quantify, however, due to suspected warm biases in the CRU data. The RCM overestimates surface insolation and outgoing longwave radiation at the top of the atmosphere (OLR-TOA). The errors in the simulated radiation are smaller over the land than the ocean. Both simulated and observed OLR-TOA suggest strong influence of low-level temperatures on the seasonal variations of OLR-TOA in the region. The results suggest that the RCM employed in this study possesses reasonable skill for studying regional climate change signals in the western United States.
Abstract
To understand the regional impact of the atmospheric aerosols on the surface energy and water cycle in the southern Sierra Nevada characterized by extreme variations in terrain elevation, the authors examine the aerosol radiative forcing on surface insolation and snowmelt for the spring of 1998 in a regional climate model experiment. With a prescribed aerosol optical thickness of 0.2, it is found that direct aerosol radiative forcing influences spring snowmelt primarily by reducing surface insolation and that these forcings on surface insolation and snowmelt vary strongly following terrain elevation. The direct aerosol radiative forcing on surface insolation is negative in all elevations. It is nearly uniform in the regions below 2000 m and decreases with increasing elevation in the region above 2000 m. This elevation dependency in the direct aerosol radiative forcing on surface insolation is related to the fact that the amount of cloud water and the frequency of cloud formation are nearly uniform in the lower elevation region, but increase with increasing elevation in the higher elevation region. This also suggests that clouds can effectively mask the direct aerosol radiative forcing on surface insolation. The direct aerosol radiative forcing on snowmelt is notable only in the regions above 2000 m and is primarily via the reduction in the surface insolation by aerosols. The effect of this forcing on low-level air temperature is as large as −0.3°C, but its impact on snowmelt is small because the sensible heat flux change is much smaller than the insolation change. The direct aerosol radiative forcing on snowmelt is significant only when low-level temperature is near the freezing point, between −3° and 5°C. When low-level temperature is outside this range, the direct aerosol radiative forcing on surface insolation has only a weak influence on snowmelt. The elevation dependency of the direct aerosol radiative forcing on snowmelt is related with this low-level temperature effect as the occurrence of the favored temperature range is most frequent in high elevation regions.
Abstract
To understand the regional impact of the atmospheric aerosols on the surface energy and water cycle in the southern Sierra Nevada characterized by extreme variations in terrain elevation, the authors examine the aerosol radiative forcing on surface insolation and snowmelt for the spring of 1998 in a regional climate model experiment. With a prescribed aerosol optical thickness of 0.2, it is found that direct aerosol radiative forcing influences spring snowmelt primarily by reducing surface insolation and that these forcings on surface insolation and snowmelt vary strongly following terrain elevation. The direct aerosol radiative forcing on surface insolation is negative in all elevations. It is nearly uniform in the regions below 2000 m and decreases with increasing elevation in the region above 2000 m. This elevation dependency in the direct aerosol radiative forcing on surface insolation is related to the fact that the amount of cloud water and the frequency of cloud formation are nearly uniform in the lower elevation region, but increase with increasing elevation in the higher elevation region. This also suggests that clouds can effectively mask the direct aerosol radiative forcing on surface insolation. The direct aerosol radiative forcing on snowmelt is notable only in the regions above 2000 m and is primarily via the reduction in the surface insolation by aerosols. The effect of this forcing on low-level air temperature is as large as −0.3°C, but its impact on snowmelt is small because the sensible heat flux change is much smaller than the insolation change. The direct aerosol radiative forcing on snowmelt is significant only when low-level temperature is near the freezing point, between −3° and 5°C. When low-level temperature is outside this range, the direct aerosol radiative forcing on surface insolation has only a weak influence on snowmelt. The elevation dependency of the direct aerosol radiative forcing on snowmelt is related with this low-level temperature effect as the occurrence of the favored temperature range is most frequent in high elevation regions.
Abstract
A Monte Carlo framework is adopted for propagating uncertainty in dynamically downscaled seasonal forecasts of area-averaged daily precipitation to associated streamflow response calculations. Daily precipitation is modeled as a mixture of two stochastic processes: a binary occurrence process and a continuous intensity process, both exhibiting serial correlation. The parameters of these processes (e.g., the proportion of wet days and the average wet-day precipitation intensity in a month) are derived from the forecast record. Parameter uncertainty is characterized via an empirical Bayesian model, whereby such parameters are modeled as random with a specific joint probability distribution. The hyperparameters specifying this probability distribution are derived from historical precipitation records at the study basin. Simulated parameter values are then generated using the Bayesian model, leading to alternative synthetic daily precipitation records simulated via the stochastic precipitation model. The set of such synthetic precipitation records is finally input to a physically based deterministic hydrologic model for propagating uncertainty in forecasted precipitation to hydrologic impact assessment studies.
The stochastic simulation approach is applied for generating an ensemble (set) of synthetic area-averaged daily precipitation records at the Hopland basin in the northern California Coast Range for the winter months (December through February: DJF) of 1997/98. The parameters of the stochastic precipitation model are derived from a seasonal precipitation forecast based on the Regional Climate System Model (RCSM), available at a 36-km2 grid spacing. The large-scale forcing input to RCSM for dynamical downscaling was a seasonal prediction of the University of California, Los Angeles, Atmospheric General Circulation Model. A semidistributed deterministic hydrologic model (“TOPMODEL”) is then used for calculating the streamflow response for each member of the area-averaged precipitation ensemble set. Uncertainty in the parameters of the stochastic precipitation model is finally propagated to associated streamflow response, by considering parameter values derived from historical (DJF 1958–92) area-averaged precipitation records at Hopland.
Abstract
A Monte Carlo framework is adopted for propagating uncertainty in dynamically downscaled seasonal forecasts of area-averaged daily precipitation to associated streamflow response calculations. Daily precipitation is modeled as a mixture of two stochastic processes: a binary occurrence process and a continuous intensity process, both exhibiting serial correlation. The parameters of these processes (e.g., the proportion of wet days and the average wet-day precipitation intensity in a month) are derived from the forecast record. Parameter uncertainty is characterized via an empirical Bayesian model, whereby such parameters are modeled as random with a specific joint probability distribution. The hyperparameters specifying this probability distribution are derived from historical precipitation records at the study basin. Simulated parameter values are then generated using the Bayesian model, leading to alternative synthetic daily precipitation records simulated via the stochastic precipitation model. The set of such synthetic precipitation records is finally input to a physically based deterministic hydrologic model for propagating uncertainty in forecasted precipitation to hydrologic impact assessment studies.
The stochastic simulation approach is applied for generating an ensemble (set) of synthetic area-averaged daily precipitation records at the Hopland basin in the northern California Coast Range for the winter months (December through February: DJF) of 1997/98. The parameters of the stochastic precipitation model are derived from a seasonal precipitation forecast based on the Regional Climate System Model (RCSM), available at a 36-km2 grid spacing. The large-scale forcing input to RCSM for dynamical downscaling was a seasonal prediction of the University of California, Los Angeles, Atmospheric General Circulation Model. A semidistributed deterministic hydrologic model (“TOPMODEL”) is then used for calculating the streamflow response for each member of the area-averaged precipitation ensemble set. Uncertainty in the parameters of the stochastic precipitation model is finally propagated to associated streamflow response, by considering parameter values derived from historical (DJF 1958–92) area-averaged precipitation records at Hopland.
Abstract
The authors present a seasonal hindcast and prediction of precipitation in the western United States and stream flow in a northern California coastal basin for December 1997–February 1998 (DJF) using the Regional Climate System Model (RCSM). In the seasonal hindcast simulation, in which the twice-daily National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis was used for the initial conditions and time-dependent boundary forcing, RCSM has simulated realistically the temporal and spatial variations of precipitation in California and stream flow in a northern California coastal basin. For the headwater basin of the Russian River in the northern California Coast Ranges, the Topography-Based Hydrologic Model (TOPMODEL) forced by observed daily precipitation resulted in a correlation coefficient of 0.88 between observed and simulated DJF stream flow. In the coupled stream flow hindcast, the authors obtained a correlation coefficient of 0.7 between simulated and observed stream flow for the same period. The coupled hindcast has generally overestimated (underestimated) low (high) flow events in the basin. Errors in the simulated stream flow were due mostly to the errors in the simulated precipitation. A seasonal hydroclimate prediction experiment, in which RCSM was nested within the global forecast data from the University of California, Los Angeles, GCM, has predicted well the season-total precipitation in the western United States. Temporal variations of predicted precipitation were affected strongly by the predictability of the general circulation model. The predicted DJF-total snowfall agrees well with the snowfall simulated in the hindcast, especially in the central Cascades and the Sierra Nevada, where snowfall was the heaviest.
Abstract
The authors present a seasonal hindcast and prediction of precipitation in the western United States and stream flow in a northern California coastal basin for December 1997–February 1998 (DJF) using the Regional Climate System Model (RCSM). In the seasonal hindcast simulation, in which the twice-daily National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis was used for the initial conditions and time-dependent boundary forcing, RCSM has simulated realistically the temporal and spatial variations of precipitation in California and stream flow in a northern California coastal basin. For the headwater basin of the Russian River in the northern California Coast Ranges, the Topography-Based Hydrologic Model (TOPMODEL) forced by observed daily precipitation resulted in a correlation coefficient of 0.88 between observed and simulated DJF stream flow. In the coupled stream flow hindcast, the authors obtained a correlation coefficient of 0.7 between simulated and observed stream flow for the same period. The coupled hindcast has generally overestimated (underestimated) low (high) flow events in the basin. Errors in the simulated stream flow were due mostly to the errors in the simulated precipitation. A seasonal hydroclimate prediction experiment, in which RCSM was nested within the global forecast data from the University of California, Los Angeles, GCM, has predicted well the season-total precipitation in the western United States. Temporal variations of predicted precipitation were affected strongly by the predictability of the general circulation model. The predicted DJF-total snowfall agrees well with the snowfall simulated in the hindcast, especially in the central Cascades and the Sierra Nevada, where snowfall was the heaviest.
Abstract
Atmospheric rivers (ARs) are long and narrow regions of strong horizontal water vapor transport. Upon landfall, ARs are typically associated with heavy precipitation and strong surface winds. A quantitative understanding of the atmospheric conditions that favor extreme surface winds during ARs has implications for anticipating and managing various impacts associated with these potentially hazardous events. Here, a global AR database (1999–2014) with relevant information from MERRA-2 reanalysis, QuikSCAT, and AIRS satellite observations is used to better understand and quantify the role of near-surface static stability in modulating surface winds during landfalling ARs. The temperature difference between the surface and 1 km MSL (ΔT; used here as a proxy for near-surface static stability), along with integrated water vapor transport (IVT), is analyzed to quantify their relationships to surface winds using bivariate linear regression. In four regions where AR landfalls are common, the MERRA-2-based results indicate that IVT accounts for 22%–38% of the variance in surface wind speed. Combining ΔT with IVT increases the explained variance to 36%–52%. Substitution of QuikSCAT surface winds and AIRS ΔT in place of the MERRA-2 data largely preserves this relationship (e.g., 44% as compared with 52% explained variance for U.S. West Coast). Use of an alternate static stability measure—the bulk Richardson number—yields a similar explained variance (47%). Last, AR cases within the top and bottom 25% of near-surface static stability indicate that extreme surface winds (gale or higher) are more likely to occur in unstable conditions (5.3% and 14.7% during weak and strong IVT, respectively) than in stable conditions (0.58% and 6.15%).
Abstract
Atmospheric rivers (ARs) are long and narrow regions of strong horizontal water vapor transport. Upon landfall, ARs are typically associated with heavy precipitation and strong surface winds. A quantitative understanding of the atmospheric conditions that favor extreme surface winds during ARs has implications for anticipating and managing various impacts associated with these potentially hazardous events. Here, a global AR database (1999–2014) with relevant information from MERRA-2 reanalysis, QuikSCAT, and AIRS satellite observations is used to better understand and quantify the role of near-surface static stability in modulating surface winds during landfalling ARs. The temperature difference between the surface and 1 km MSL (ΔT; used here as a proxy for near-surface static stability), along with integrated water vapor transport (IVT), is analyzed to quantify their relationships to surface winds using bivariate linear regression. In four regions where AR landfalls are common, the MERRA-2-based results indicate that IVT accounts for 22%–38% of the variance in surface wind speed. Combining ΔT with IVT increases the explained variance to 36%–52%. Substitution of QuikSCAT surface winds and AIRS ΔT in place of the MERRA-2 data largely preserves this relationship (e.g., 44% as compared with 52% explained variance for U.S. West Coast). Use of an alternate static stability measure—the bulk Richardson number—yields a similar explained variance (47%). Last, AR cases within the top and bottom 25% of near-surface static stability indicate that extreme surface winds (gale or higher) are more likely to occur in unstable conditions (5.3% and 14.7% during weak and strong IVT, respectively) than in stable conditions (0.58% and 6.15%).
Abstract
Several dynamically downscaled climate simulations with various spatial resolutions (24, 12, and 4 km) and spectral nudging strengths (0, 600, and 2000 km) have been run over the contiguous United States from 2000 to 2009 using the high-resolution NASA Unified Weather and Research Forecasting (NU-WRF) regional model initialized and constrained by the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). This paper summarizes the authors’ efforts on the development of a model performance metric and its application to assess summer precipitation over the U.S. Great Plains (USGP) in these downscaled climate simulations. A new model performance metric T was first developed that uses both the linear correlation coefficient and mean square error and is consistent with other commonly used metrics, but gives a bigger separation between good and bad simulations. This metric T was then applied to the summer mean precipitation spatial pattern, diurnal Hovmöller diagram, and diurnal spatial pattern over the USGP from the simulations focusing on the summer precipitation diurnal cycle related to mesoscale convective systems (MCSs). The metric T skill scores increase significantly from the control simulation to the nudged simulations and from the nudged simulations with shorter wavelengths to the nudged simulations with longer wavelengths, but do not change much from MERRA-2 to the downscaled simulations or between the various downscaled simulations with different spatial resolutions. Thus, there is some credibility, but no significant value added compared to MERRA-2, of the downscaled climate simulations of the summer precipitation over the USGP.
Abstract
Several dynamically downscaled climate simulations with various spatial resolutions (24, 12, and 4 km) and spectral nudging strengths (0, 600, and 2000 km) have been run over the contiguous United States from 2000 to 2009 using the high-resolution NASA Unified Weather and Research Forecasting (NU-WRF) regional model initialized and constrained by the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). This paper summarizes the authors’ efforts on the development of a model performance metric and its application to assess summer precipitation over the U.S. Great Plains (USGP) in these downscaled climate simulations. A new model performance metric T was first developed that uses both the linear correlation coefficient and mean square error and is consistent with other commonly used metrics, but gives a bigger separation between good and bad simulations. This metric T was then applied to the summer mean precipitation spatial pattern, diurnal Hovmöller diagram, and diurnal spatial pattern over the USGP from the simulations focusing on the summer precipitation diurnal cycle related to mesoscale convective systems (MCSs). The metric T skill scores increase significantly from the control simulation to the nudged simulations and from the nudged simulations with shorter wavelengths to the nudged simulations with longer wavelengths, but do not change much from MERRA-2 to the downscaled simulations or between the various downscaled simulations with different spatial resolutions. Thus, there is some credibility, but no significant value added compared to MERRA-2, of the downscaled climate simulations of the summer precipitation over the USGP.
Abstract
This study investigates the sensitivity of daily rainfall rates in regional seasonal simulations over the contiguous United States (CONUS) to different cumulus parameterization schemes. Daily rainfall fields were simulated at 24-km resolution using the NASA-Unified Weather Research and Forecasting (NU-WRF) Model for June–August 2000. Four cumulus parameterization schemes and two options for shallow cumulus components in a specific scheme were tested. The spread in the domain-mean rainfall rates across the parameterization schemes was generally consistent between the entire CONUS and most subregions. The selection of the shallow cumulus component in a specific scheme had more impact than that of the four cumulus parameterization schemes. Regional variability in the performance of each scheme was assessed by calculating optimally weighted ensembles that minimize full root-mean-square errors against reference datasets. The spatial pattern of the seasonally averaged rainfall was insensitive to the selection of cumulus parameterization over mountainous regions because of the topographical pattern constraint, so that the simulation errors were mostly attributed to the overall bias there. In contrast, the spatial patterns over the Great Plains regions as well as the temporal variation over most parts of the CONUS were relatively sensitive to cumulus parameterization selection. Overall, adopting a single simulation result was preferable to generating a better ensemble for the seasonally averaged daily rainfall simulation, as long as their overall biases had the same positive or negative sign. However, an ensemble of multiple simulation results was more effective in reducing errors in the case of also considering temporal variation.
Abstract
This study investigates the sensitivity of daily rainfall rates in regional seasonal simulations over the contiguous United States (CONUS) to different cumulus parameterization schemes. Daily rainfall fields were simulated at 24-km resolution using the NASA-Unified Weather Research and Forecasting (NU-WRF) Model for June–August 2000. Four cumulus parameterization schemes and two options for shallow cumulus components in a specific scheme were tested. The spread in the domain-mean rainfall rates across the parameterization schemes was generally consistent between the entire CONUS and most subregions. The selection of the shallow cumulus component in a specific scheme had more impact than that of the four cumulus parameterization schemes. Regional variability in the performance of each scheme was assessed by calculating optimally weighted ensembles that minimize full root-mean-square errors against reference datasets. The spatial pattern of the seasonally averaged rainfall was insensitive to the selection of cumulus parameterization over mountainous regions because of the topographical pattern constraint, so that the simulation errors were mostly attributed to the overall bias there. In contrast, the spatial patterns over the Great Plains regions as well as the temporal variation over most parts of the CONUS were relatively sensitive to cumulus parameterization selection. Overall, adopting a single simulation result was preferable to generating a better ensemble for the seasonally averaged daily rainfall simulation, as long as their overall biases had the same positive or negative sign. However, an ensemble of multiple simulation results was more effective in reducing errors in the case of also considering temporal variation.
Abstract
The Project for Intercomparison of Land-Surface Parameterization Schemes phase 2(d) experiment at Valdai, Russia, offers a unique opportunity to evaluate land surface schemes, especially snow and frozen soil parameterizations. Here, the ability of the 21 schemes that participated in the experiment to correctly simulate the thermal and hydrological properties of the soil on several different timescales was examined. Using observed vertical profiles of soil temperature and soil moisture, the impact of frozen soil schemes in the land surface models on the soil temperature and soil moisture simulations was evaluated.
It was found that when soil-water freezing is explicitly included in a model, it improves the simulation of soil temperature and its variability at seasonal and interannual scales. Although change of thermal conductivity of the soil also affects soil temperature simulation, this effect is rather weak. The impact of frozen soil on soil moisture is inconclusive in this experiment due to the particular climate at Valdai, where the top 1 m of soil is very close to saturation during winter and the range for soil moisture changes at the time of snowmelt is very limited. The results also imply that inclusion of explicit snow processes in the models would contribute to substantially improved simulations. More sophisticated snow models based on snow physics tend to produce better snow simulations, especially of snow ablation. Hysteresis of snow-cover fraction as a function of snow depth is observed at the catchment but not in any of the models.
Abstract
The Project for Intercomparison of Land-Surface Parameterization Schemes phase 2(d) experiment at Valdai, Russia, offers a unique opportunity to evaluate land surface schemes, especially snow and frozen soil parameterizations. Here, the ability of the 21 schemes that participated in the experiment to correctly simulate the thermal and hydrological properties of the soil on several different timescales was examined. Using observed vertical profiles of soil temperature and soil moisture, the impact of frozen soil schemes in the land surface models on the soil temperature and soil moisture simulations was evaluated.
It was found that when soil-water freezing is explicitly included in a model, it improves the simulation of soil temperature and its variability at seasonal and interannual scales. Although change of thermal conductivity of the soil also affects soil temperature simulation, this effect is rather weak. The impact of frozen soil on soil moisture is inconclusive in this experiment due to the particular climate at Valdai, where the top 1 m of soil is very close to saturation during winter and the range for soil moisture changes at the time of snowmelt is very limited. The results also imply that inclusion of explicit snow processes in the models would contribute to substantially improved simulations. More sophisticated snow models based on snow physics tend to produce better snow simulations, especially of snow ablation. Hysteresis of snow-cover fraction as a function of snow depth is observed at the catchment but not in any of the models.