1. Introduction
Precipitation phase partitioning is crucial to the understanding of the land hydrological process, the water and energy nexus, climate change, water resources management, and disaster monitoring (Behrangi et al. 2018; Wen et al. 2017). Rainfall and snowfall have distinct hydrological and climatological impacts over both land and ocean (Behrangi et al. 2017; Liu 2008; Tang et al. 2017b). Unlike runoff generation and routing processes of rainfall, snowfall contributes to ground snow storage and affects interception, evaporation, infiltration, and the time and magnitude of peak flow and base flow (Safeeq et al. 2014; Wang et al. 2016).
Since the coverage of surface weather stations is limited, satellite remote sensing is the only practical way of obtaining global rainfall and snowfall data (Sims and Liu 2015). However, precipitation phase determination has been challenging for satellite remote sensing. The most common approach is estimating precipitation intensity first and then separating rainfall and snowfall using various precipitation phase partitioning methods (PPMs; (Behrangi et al. 2018). Typically, PPMs rely on air temperature Ta (Harpold et al. 2017), while other factors such as relative humidity (RH) and wind speed also have some impact. Compared to Ta, the wet-bulb temperature Tw as a function of Ta and RH is a closer approximation of the actual temperature of precipitation particles (Stull 2011). Many studies indicate that humidity-dependent methods such as those based on Tw (Harpold et al. 2017) lead to better rain–snow classification than those only based on Ta (Behrangi et al. 2018; Froidurot et al. 2014; Harder and Pomeroy 2013; Sims and Liu 2015; Ye et al. 2013).
The Tw-based PPM is also adopted by the Integrated Multisatellite Retrievals for Global Precipitation Measurement (IMERG; Huffman et al. 2017), which provides the first blended global satellite precipitation product distinguishing rainfall and snowfall. IMERG data cover 60°S–60°N at 0.1° × 0.1° and 30-min resolutions and generally perform better than their predecessor, that is, Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA; Tang et al. 2018, 2017a, 2016). The IMERG algorithm provides three types of products—the Early, Late, and Final runs—to meet different research and application requirements. The near-real-time Early and Late runs have small latency time of ~4 and ~12 h, respectively, while their quality is generally worse than the gauge-adjusted Final run with latency time of ~2.5 months. The PPM adopted by IMERG uses a lookup table as a function of Tw (Huffman et al. 2017) based on Sims and Liu (2015). Auxiliary data of Ta, RH, and surface pressure for phase partitioning are provided by the Japanese Meteorological Agency (JMA) forecasts (for the Early and Late runs) and the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis (ERA-Interim; for the Final run).
However, reanalysis products have the disadvantage of coarse spatial resolutions. For example, ERA-Interim data have a native horizontal resolution of ~80 km, which is much coarser compared to the 0.1° resolution of IMERG. Direct application of coarse-resolution data cannot depict subgrid variation resulting in suboptimal rain–snow partitioning, particularly in heterogeneous terrains where temperature shows strong spatial variability. Therefore, it is necessary to develop more advanced downscaling techniques that can help acquire better high-resolution data than purely statistical interpolation methods (Ma et al. 2017). Air temperature has a good relationship with elevation and can be downscaled based on temperature lapse rate (TLR; Bieniek et al. 2016; Gardner et al. 2009). Through the downscaling of reanalysis Ta, the quality of Tw is also anticipated to be improved because Tw is calculated from Ta and RH.
Traditionally, Ta is assumed to decrease linearly with elevation with a constant TLR value, such as −6.5°C km−1 (Hamlet and Lettenmaier 2005; Lundquist and Cayan 2007; Maurer et al. 2002), whereas sometimes the phenomenon could be reversed with temperature increasing with elevation (Gardner et al. 2009; Sims and Liu 2015). In reality, TLR exhibits strong spatiotemporal variability due to the effect of topography, vegetation, synoptic circulation, radiation intensity, and diurnal variations (Gao et al. 2012; Minder et al. 2010; Rajagopal and Harpold 2016). Observations from dense meteorological stations can capture the variability of TLR, which, however, is impractical in most land areas with limited numbers of stations (Gao et al. 2017). Several strategies have been proposed using reanalysis temperature data at different pressure levels to calculate free-air TLR and downscale near-surface reanalysis Ta. For example, Mokhov and Akperov (2006) acquired TLR based on temperature data at 12 pressure levels (from 100 to 1000 hPa) from National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) via linear regression. Gerlitz et al. (2014) built the relationship between temperature and geopotential heights at different pressure levels using a polynomial regression and acquired near-surface temperature based on the regression equation. Gao et al. (2012) compared various methods for calculating TLR and downscaled ERA-Interim temperature to meteorological stations at the point scale in German and Swiss Alps.
Dynamical downscaling of Ta using regional climate models is another choice; however, it is too complex and computationally challenging (Gardner et al. 2009). In contrast, TLR-based temperature downscaling is easy to implement and computationally efficient, which is more suitable for the operational application in the IMERG system, particularly for the near-real-time Early and Late runs. The accuracy of high-resolution Tw can also be improved benefiting from the downscaling of Ta, which can contribute to the improvement of rain–snow partitioning of IMERG. However, to our knowledge, there is no study exploring the benefits brought by downscaled Ta to Tw and rain–snow partitioning, which can hopefully improve the accuracy of the precipitation phase of satellite precipitation products such as IMERG.
Therefore, the objectives of this study are to 1) evaluate and compare the performance of different Ta downscaling methods in the contiguous United States (CONUS), 2) assess the quality of Tw derived from downscaled Ta, and 3) investigate the benefits to rain–snow partitioning brought by the temperature downscaling techniques. The paper is organized as follows. Section 2 introduces reanalysis and ground-based observation datasets. Section 3 demonstrates downscaling and rain–snow partitioning methods, as well as the statistical metrics. Section 4 presents results, followed by the summary and conclusions section.
2. Data
a. ERA-Interim
b. PRISM
The PRISM AN81d data record (Daly et al. 1994, 2008) provides Ta, Td, and precipitation from 2010 to 2015 at 4-km and daily resolutions in the CONUS. PRISM utilizes data from a large number of sources, such as the National Weather Service Cooperative Observer Program (COOP) and U.S. Department of Agriculture (USDA) Natural Resources Conservation Service Snowpack Telemetry (SNOTEL). The number of meteorological stations used in PRISM is nearly 13 000 for precipitation and nearly 10 000 for minimum and maximum temperature (Daly et al. 2008). PRISM data are taken as the benchmark in the validation of downscaled ERA-Interim temperature because of its widely recognized quality on the basis of sophisticated mapping techniques and solid ground observation records.
c. SNODAS
Snowfall data are from the Snow Data Assimilation System (SNODAS) developed by the National Oceanic and Atmospheric Administration (NOAA) National Weather Service’s National Operational Hydrologic Remote Sensing Center (NOHRSC; Barrett 2003). SNODAS data are averaged to 0.1° from the original resolution of 1 km in the CONUS. SNODAS utilizes data from satellite, airborne, and ground observations combined with a physically based, spatially distributed energy and mass balance snow model. A series of snow-related variables are provided, such as snow water equivalent (SWE), snow depth, sublimation, and solid/liquid precipitation. SNODAS data are used to assess the performance of rain–snow partitioning. However, the uncertainties of SNODAS snowfall data and the effect on evaluation results are not quantified in this study because of the lack of snowfall observations.
d. DEM
Digital elevation model (DEM) data with a resolution of 1 km (30 s) from Hydrological Data and Maps Based on Shuttle Elevation Derivatives at Multiple Scales (HydroSHEDS) are used (https://hydrosheds.cr.usgs.gov). Coarse-resolution DEM is resampled from the 1-km data.
3. Methods
a. Framework design
Figure 1 shows the framework of this study. Overall, the study was conducted in three steps. First, original ERA-Interim Ta with a resolution of 0.75° was downscaled to 0.1° using eight methods as introduced in section 3b. The target resolution was determined as 0.1° in accordance with IMERG precipitation data. PRISM Ta was also resampled from 4 km to 0.1° and used to evaluate the performance of the downscaled ERA-Interim Ta. Second, ERA-Interim Td was downscaled to 0.1° using linear interpolation since there is no recognized downscaling method for Td due to its complex variation mechanism. RH with a resolution of 0.1° was calculated using downscaled Td and Ta based on Eq. (3). Based on downscaled Ta and RH, we acquired Tw using Eq. (4) which was evaluated using PRISM-based Tw. Third, rainfall and snowfall were classified using ERA-Interim-based and PRISM-based Tw. Rain–snow partitioning results are evaluated using SNODAS snowfall data as the benchmark and are also compared to IMERG precipitation phase.
A flow diagram showing the processes of Ta downscaling, Tw calculation, and rain–snow classification.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
A flow diagram showing the processes of Ta downscaling, Tw calculation, and rain–snow classification.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
A flow diagram showing the processes of Ta downscaling, Tw calculation, and rain–snow classification.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
By means of the three steps of comparison and evaluation, we demonstrated the improvement of TLR-based downscaling methods relative to purely statistical methods and the implications for rain–snow classification.
b. Air temperature downscaling
Eight Ta downscaling methods are used in this study. Methods 1 and 2 are purely statistical interpolation methods. Reanalysis temperature is directly interpolated from 0.75° to 0.1°. The first method is nearest neighbor (NN). The second method is bilinear interpolation (BI), which is used in the current IMERG algorithm (David Bolvin, IMERG Team, 2018, personal communication).
Method 3 is fixed TLR (FTLR). A fixed TLR value (−6.5°C km−1) is adopted in the entire CONUS and during all seasons (Hamlet and Lettenmaier 2005; Lundquist and Cayan 2007; Maurer et al. 2002).
Method 5 is MA_TLR, where TLR values are linearly regressed using ERA-Interim temperature and geopotential heights at 14 pressure levels at the resolution of 0.75° (Mokhov and Akperov 2006).
Method 6 is Gruber_TLR. This method adopts TLR values from MA_TLR, while the downscaling process is more complex. Coarse-resolution temperature is first reduced from current elevation to sea level using Eq. (5). Then, the temperature is interpolated to 0.1° using BI directly because all grid pixels are at the height of sea level. Finally, the temperature field with a resolution of 0.1° is readjusted to actual surface elevation using Eq. (5) again (Gruber 2012).
Method 8 is PRISM TLR (PTLR). Unlike the other TLR-based methods relying on ERA-Interim data, TLR of this method is linearly regressed using PRISM temperature and altitude from all of the nested 4-km grid pixels contained in each 0.75° grid pixel. Then, Ta is calculated using Eq. (5) just like methods 3–5.
c. Rain–snow partitioning
Behrangi et al. (2018) and Sims and Liu (2015) show that Tw yields higher skill scores than other single predictors (such as Ta or Td) for rain–snow partitioning. Moreover, Behrangi et al. (2018) shows that the critical threshold of Tw (CTw) has smaller regional variation than that of Ta. For simplicity, the study uses a static CTw (0°C) for rain–snow partitioning. Precipitation with Tw smaller than CTw is classified as snowfall. We also tested other CTw values and discussed the results in the following sections.
d. Metrics
To evaluate the performance of downscaled ERA-Interim temperature, we utilized metrics including correlation coefficient (CC), mean error (ME), relative bias (BIAS), and root-mean-square error (RMSE). To avoid offset between negative and positive errors, mean absolute error (MAE) and absolute relative bias (ABIAS) are also considered. Furthermore, four contingency metrics are used to demonstrate the performance of rain–snow partitioning based on ERA-Interim Tw, including the probability of detection (POD), false alarm ratio (FAR), critical success index (CSI) as a function of POD and FAR, and Heidke skill score (HSS) representing the accuracy of the variable relative to that of random forecast. Formulas and perfect values of these metrics are in Table 1. These metrics are calculated at each 0.1° grid pixel in the CONUS and then aggregated to acquire mean areal values.
The formulas, value ranges, and perfect values of the metrics used in this study. Parameters 
4. Results
a. Air temperature downscaling and evaluation
Figure 2 shows the spatial distributions of mean Ta and Td from 2010 to 2015. PRISM and ERA-Interim capture the pattern of Ta decreasing from south to north in the CONUS. The Rocky Mountains are characterized by much lower Ta than other regions. California and southern Arizona are hot regions in the western United States (defined as regions west of 105°W in this study). The dewpoint temperature Td is much lower than Ta. Their mean values are 2.9° and 11.5°C in the CONUS, respectively. In addition, Td exhibits different spatial distributions from Ta, particularly in the western United States, where Td is particularly low due to the effect of complex topography and relatively arid climate. ERA-Interim agrees well with PRISM in terms of spatial distributions and temperature magnitudes, although the coarse resolution of ERA-Interim hampers detailed representation of temperature variation caused by topography.
Spatial distributions of mean (left) Ta and (right) Td of (a),(b) PRISM at 4-km resolution and (c),(d) ERA-Interim at 0.75° resolution. The period is from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of mean (left) Ta and (right) Td of (a),(b) PRISM at 4-km resolution and (c),(d) ERA-Interim at 0.75° resolution. The period is from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of mean (left) Ta and (right) Td of (a),(b) PRISM at 4-km resolution and (c),(d) ERA-Interim at 0.75° resolution. The period is from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
The differences between downscaled ERA-Interim Ta and PRISM Ta at the resolution of 0.1° are shown in Fig. 3. According to all these methods except Gerlitz_regression, ERA-Interim exhibits a mixed distribution of underestimation and overestimation of Ta in the western United States and notable overestimation in the central United States. We further conducted seasonal analysis and found that the cold bias in the western United States mainly occurs in cold seasons (January–March), and the warm bias mainly occurs in warm seasons (June–September). A possible explanation is that ERA-Interim has fixed values of LAI, which depend only on vegetation types. LAI in cold seasons is larger than reality, leading to larger evaporation and lower surface temperature (Betts and Beljaars 2017), and vice versa in warm seasons.
(a)–(h) Spatial distributions of ME for ERA-Interim Ta based on eight downscaling methods using PRISM Ta as the benchmark at the resolution of 0.1° from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
(a)–(h) Spatial distributions of ME for ERA-Interim Ta based on eight downscaling methods using PRISM Ta as the benchmark at the resolution of 0.1° from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
(a)–(h) Spatial distributions of ME for ERA-Interim Ta based on eight downscaling methods using PRISM Ta as the benchmark at the resolution of 0.1° from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
It is noted that the ME of all the downscaling methods is characterized by mosaic distributions except for BI and Gruber_TLR (Figs. 3b,f) because BI and Gruber_TLR utilize linear interpolation while the other downscaling methods are conducted for each 0.75° grid pixel separately. Temperature Ta based on NN and BI shows similar ME distributions indicating that the two purely statistical methods cannot help improve the quality of ERA-Interim data. The Ta based on five TLR-based downscaling methods reduces ME compared to NN and BI (Figs. 3c–f,h). Gerlitz_regression exhibits the largest warm bias compared to other methods, particularly in the western and central United States (Fig. 3g), which is consistent with the results in Gao et al. (2017). Therefore, the regressed relationships using temperature and geopotential heights at different pressure levels cannot be directly applied to Ta at the near-surface level.
Table 2 summarizes the metrics of downscaled ERA-Interim Ta, which are calculated for each grid pixel and averaged in the CONUS and western United States. The western United States is listed separately because its complex topography could greatly affect the quality of ERA-Interim temperature and downscaling methods. All the methods show excellent and similar CC (~0.97) except for Gerlitz_regression, indicating that ERA-Interim can capture the temporal variation of temperature pretty well. Compared to NN and BI, TLR-based downscaling methods improve the accuracy of Ta, particularly in the western United States, where the rugged topography contributes to more robust temperature–altitude relationships and the rationalities of TLR-based downscaling. As anticipated, PTLR-based Ta is the closest to PRISM Ta because it utilizes PRISM data. The ABIAS and MAE (10.71% and 0.78°C) of PTLR-based Ta are much smaller than those (19.07% and 1.18°C) of NN-based Ta in the western United States. Gruber_TLR is the second best compared to other TLR-based methods, with the ABIAS of 12.39% and MAE of 0.82°C in the western United States. MA_TLR is slightly worse than Gao_TLR because the relationship between temperature and geopotential heights varies with time, space, and heights and sometimes cannot be depicted by linear regression well.
Metrics of the eight sets of downscaled ERA-Interim Ta in the CONUS and the western United States benchmarked by the PRISM Ta. The bold numbers correspond to the best metrics among all methods.
According to the aforementioned validation and comparison of downscaled Ta, TLR-based downscaling methods perform better than NN and BI, while Gerlitz_regression shows great overestimation. Different methods have large discrepancies in the western United States compared to the eastern United States. Therefore, we selected two representative methods, that is, NN and Gruber_TLR, to study their performance in six typical mountain ranges in the western United States. The mountains include the Cascade Range (122.6°–120.4°W, 47.1°–49°N), Bighorn Mountain (108.3°–106.4°W, 43.3°–45.3°N), Black Hills (104.8°–102.8°W, 43.2°–44.8°N), Uinta Mountains (114.4°–112.1°W, 40.1°–41.3°N), Sierra Nevada (120.4°–118.4°W, 36.3°–38.7°N), and Edwards Plateau (104.7°–102.4°W, 28.9°–31.1°N). The locations are shown in Fig. 4. For simplicity, for each mountain range, the analysis was performed on a rectangular region. ME of NN-based Ta shows a strong correlation with elevation, indicating that ERA-Interim temperature contains topography-dependent systematic errors (Fig. 5). NN obviously overestimates Ta in mountains with higher elevations but underestimates Ta in surrounding plains and valleys with lower elevations. BI also has the similar problem with NN. In contrast, Gruber_TLR greatly reduces the overestimation in mountains and the underestimation in the Central Valley next to the Sierra Nevada (Fig. 5), indicating that TLR-based downscaling methods are very effective in mountainous regions. Nevertheless, it should also be noted that the ME of Gruber_TLR is reversed compared to that of NN in some areas, such as the slight underestimation in the Uinta Mountains and overestimation in its southern plains. A possible explanation is that TLR values could be too large for such areas. Better characterization of TLR in both space and time is necessary for better temperature downscaling, which is worth exploring in future studies.
The DEM map of the western United States and the locations of six selected mountain ranges in the CONUS. Boxes 1–6 (B1–B6) represent the Cascade Range, Bighorn Mountain, Black Hills, Uinta Mountains, Sierra Nevada, and Edwards Plateau, respectively.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
The DEM map of the western United States and the locations of six selected mountain ranges in the CONUS. Boxes 1–6 (B1–B6) represent the Cascade Range, Bighorn Mountain, Black Hills, Uinta Mountains, Sierra Nevada, and Edwards Plateau, respectively.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
The DEM map of the western United States and the locations of six selected mountain ranges in the CONUS. Boxes 1–6 (B1–B6) represent the Cascade Range, Bighorn Mountain, Black Hills, Uinta Mountains, Sierra Nevada, and Edwards Plateau, respectively.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of (left) DEM and ME for Ta based on (center) NN and (right) Gruber_TLR downscaling methods in six typical mountain ranges.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of (left) DEM and ME for Ta based on (center) NN and (right) Gruber_TLR downscaling methods in six typical mountain ranges.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of (left) DEM and ME for Ta based on (center) NN and (right) Gruber_TLR downscaling methods in six typical mountain ranges.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
b. Wet-bulb temperature evaluation
Air temperature Ta has been downscaled from 0.75° to 0.1° based on eight different methods in section 4a. Since rain–snow partitioning is based on Tw in this study, we further calculated Tw using downscaled temperature based on Eq. (4). For simplicity, if Tw uses Ta from a specific downscaling method such as NN, we refer it as NN-based Tw. The spatial distributions of Tw based on PRISM and three selected sets of downscaled ERA-Interim temperature are shown in Fig. 6. Wet-bulb temperature Tw based on other downscaling methods is not shown because of their similar distributions with Figs. 6c and 6d. Overall, Tw is similar to Ta in terms of spatial distributions. Unlike NN-based Tw, Gruber_TLR-based Tw can reproduce the spatial variations of PRISM-based Tw, particularly in the mountainous regions in the western United States. Gerlitz_regression greatly overestimates Tw compared to other methods.
Spatial distributions of (a) mean Tw based on PRISM temperature, and mean Tw based on downscaled ERA-Interim temperature using (b) NN, (c) Gruber_TLR, and (d) Gerlitz_regression at 0.1° resolution from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of (a) mean Tw based on PRISM temperature, and mean Tw based on downscaled ERA-Interim temperature using (b) NN, (c) Gruber_TLR, and (d) Gerlitz_regression at 0.1° resolution from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of (a) mean Tw based on PRISM temperature, and mean Tw based on downscaled ERA-Interim temperature using (b) NN, (c) Gruber_TLR, and (d) Gerlitz_regression at 0.1° resolution from 2010 to 2015.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Figure 7 shows the scatterplots between mean daily PRISM-based and ERA-Interim-based Tw from 2010 to 2015. The western and eastern United States are studied separately considering their topography and climate differences. In the eastern United States, the eight sets of ERA-Interim-based Tw agree pretty well with PRISM-based Tw. Their CC is almost 1, and ABIAS is around 7%. On the whole, the eight downscaling methods do not show obvious differences in the eastern United States since they all perform reasonably well. In contrast, these methods show more differentiated performance in the western United States. Gruber_TLR is the best among the eight downscaling methods in the western United States (CC = 0.98, ABIAS = 13%, RMSE = 0.71°C). For NN and BI, the CC is reduced to 0.94, the ABIAS is increased to 20%, and the RMSE is increased to 1.2°C. Metrics of Tw based on FTLR, Gao_TLR, and MA_TLR are similar to each other. Gerlitz_regression is still the worst, with the largest ABIAS (27%) and RMSE (1.3°C) in the western United States, while the ABIAS of Gerlitz_regression is only 9% in the eastern United States.
(a)–(h) Scatterplots between mean daily PRISM- and ERA-Interim-based Tw from 2010 to 2015 for eight downscaling methods. Black circles and metrics are for regions west of 105°W, while blue dots and metrics are for regions east of 105°W. Red diagonals are the 1-to-1 lines.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
(a)–(h) Scatterplots between mean daily PRISM- and ERA-Interim-based Tw from 2010 to 2015 for eight downscaling methods. Black circles and metrics are for regions west of 105°W, while blue dots and metrics are for regions east of 105°W. Red diagonals are the 1-to-1 lines.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
(a)–(h) Scatterplots between mean daily PRISM- and ERA-Interim-based Tw from 2010 to 2015 for eight downscaling methods. Black circles and metrics are for regions west of 105°W, while blue dots and metrics are for regions east of 105°W. Red diagonals are the 1-to-1 lines.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
To demonstrate the spatial variability of the quality of Tw, Fig. 8 shows the spatial distributions of ABIAS differences between Tw from NN, Gruber_TLR, Gerlitz_regression, and PTLR and Tw from BI, which is used in IMERG. The ABIAS of BI and NN-based Tw is pretty small (Fig. 8a), while Gruber_TLR and PTLR exhibit much smaller ABIAS than BI in most areas in the western United States. In contrast, Gerlitz_regression shows much larger ABIAS than BI. In the eastern United States, ABIAS differences are close to zero because 1) the bias of original ERA-Interim is relatively small in this region, and 2) the relatively flat terrain weakens the effect of TLR-based downscaling methods.
Spatial distributions of ABIAS differences between (a) NN-, (b) Gruber_TLR-, (c) Gerlitz_regression-, and (d) PTLR-based Tw and BI-based Tw. Negative values indicate that BI has a larger ABIAS.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of ABIAS differences between (a) NN-, (b) Gruber_TLR-, (c) Gerlitz_regression-, and (d) PTLR-based Tw and BI-based Tw. Negative values indicate that BI has a larger ABIAS.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of ABIAS differences between (a) NN-, (b) Gruber_TLR-, (c) Gerlitz_regression-, and (d) PTLR-based Tw and BI-based Tw. Negative values indicate that BI has a larger ABIAS.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Table 3 compares the skill of different methods for downscaling the ERA-Interim temperature over the CONUS and western United States. CC is not involved because all downscaling methods show excellent and close values. In the CONUS, the ABIAS is reduced from ~26% of NN and BI to ~20% of the five TLR-based methods. MAE and RMSE exhibit similar patterns. Among the five TLR-based methods, Gruber_TLR is the best and even better than PTLR, which is based on ground observations. In the western United States, the discrepancies between different methods become larger. For example, the ABIAS is reduced from ~47% of NN and BI to 27.71% of Gruber_TLR, and the RMSE is reduced from ~1.9°C of NN and BI to 1.7°C of Gruber_TLR, respectively.
Comparison of the skill of different methods for downscaling the ERA-Interim temperature over the CONUS and the western United States. PRISM-based Tw serves as the comparison reference. The bold numbers correspond to the best metrics among all methods.
Precipitation phase-change usually occurs when Tw is around 0°C (Behrangi et al. 2018; Ding et al. 2014; Sims and Liu 2015). Therefore, the evaluation was also conducted for a subset of PRISM-based Tw with values between −2° and 2°C. Compared to metrics without Tw limitation (Table 3), ABIAS of all the downscaling methods increases from less than 50% to more than 250% in the western United States because the mean Tw is close to zero. Meanwhile, the improvement of TLR-based downscaling methods compared to NN and BI also becomes more notable. The RMSE (ABIAS) of NN and BI-based Tw is larger than 0.9°C (400%), whereas the RMSE (ABIAS) of Gruber_TLR-based Tw is reduced to 0.6°C (250%). The performance of NN and Gruber_TLR is further compared in six mountains because most snowfall occurs in high-altitude areas. The improvement in such regions is particularly meaningful. The results show that Gruber_TLR performs much better than NN in the six mountains (Fig. 9) benefiting from the more accurate Ta. NN tends to overestimate Tw in mountains while Gruber_TLR mitigates the problem.
Spatial distributions of (left) DEM and ME for Tw based on (center) NN and (right) Gruber_TLR downscaling methods in six typical mountain ranges.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of (left) DEM and ME for Tw based on (center) NN and (right) Gruber_TLR downscaling methods in six typical mountain ranges.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Spatial distributions of (left) DEM and ME for Tw based on (center) NN and (right) Gruber_TLR downscaling methods in six typical mountain ranges.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
On the whole, Gruber_TLR is the best with regard to Tw among all the eight downscaling methods, particularly in the western United States, which implies that TLR values based on the ERA-Interim temperature at different pressure levels are reasonable, and the downscaling processes of Gruber_TLR are effective.
c. Rain–snow partitioning assessment
Improvement of Ta and Tw using TLR-based downscaling methods is most notable in the western United States, where large topographic variation exists and snowfall frequency is relatively high. Therefore, in this section, the study region is restricted to the western United States and CTw is set to 0°C to distinguish rainfall and snowfall. In addition, considering that some downscaling methods tend to perform similarly regarding Ta and Tw, we focused on the comparison between Gruber_TLR and purely statistical methods. Please note that PRISM Tw calculated from 4-km Ta and Td is also used to separate rain and snow in this section.
The spatial distributions of SNODAS snowfall numbers and the differences compared to snowfall numbers based on Tw are shown in Fig. 10. Most snowfall events occur in mountainous regions (Fig. 10a). BI-based Tw tends to underestimate the number of snowfall events in mountains such as the Sierra Nevada and the Cascade Range and overestimates snowfall numbers in low-lying areas such as the Snake River Plain and the southern piedmont along the Cascade Range (Fig. 10b). This is because BI underestimates temperature at low elevation but overestimates temperature at high elevation. Compared to BI, Gruber_TLR-based Tw relieves the overestimation or underestimation, whereas the systematic errors of ERA-Interim temperature data cannot be completely eliminated. The number of snowfall events based on PRISM Tw is the closest to that of SNODAS, while the great underestimation in mountainous regions still exists (Fig. 10d), although PRISM temperature is based on ground observations. This is probably because the CTw (0°C) is too small for this region. We also tested other CTw values. Increasing CTw can reduce underestimation in mountainous regions, but can also add to the overestimation in low-lying areas. A spatially distributed CTw can lead to better rain–snow partitioning. This study only employs a simple rain–snow partitioning scheme to facilitate the comparison between different downscaling methods, while better schemes are needed in future studies.
(a) The number of snowfall events from 2010 to 2015 in the western United States according to SNODAS. The differences between the numbers of snowfall events of SNODAS and ERA-Interim downscaled Tw based on (b) NN, (c) Gruber_TLR, and (d) PRISM. CTw is 0°C.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
(a) The number of snowfall events from 2010 to 2015 in the western United States according to SNODAS. The differences between the numbers of snowfall events of SNODAS and ERA-Interim downscaled Tw based on (b) NN, (c) Gruber_TLR, and (d) PRISM. CTw is 0°C.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
(a) The number of snowfall events from 2010 to 2015 in the western United States according to SNODAS. The differences between the numbers of snowfall events of SNODAS and ERA-Interim downscaled Tw based on (b) NN, (c) Gruber_TLR, and (d) PRISM. CTw is 0°C.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Table 4 summarizes the metrics of rain–snow partitioning using ERA-Interim-based and PRISM-based Tw in the western United States. NN shows the least scores among all the methods. PRISM is the best with regard to all the metrics. Gruber_TLR outperforms both NN and PTLR. Note that the differences between the scores for these methods are generally quite low in the western United States. For example, CSI ranges between 0.59 and 0.64 for NN, Gruber_TLR, and PRISM, and HSS ranges between 0.62 and 0.68. Two reasons could contribute to their similar performances. First, most snowfall (rainfall) events are accompanied by much lower (higher) Tw than the CTw. For these events, the ERA-Interim temperature can correctly distinguish between rain and snow even though NN-based Tw is biased. Second, the improvement of Ta and Tw is most notable in mountainous regions, which only account for a fraction of the study region. Rain–snow partitioning in relatively flat terrain using downscaled ERA-Interim-based and PRISM-based Tw shows a similar performance, mitigating the overall improvements. Therefore, a more regional study to focus on mountain ranges seems useful.
Metrics of rain–snow partitioning using ERA-Interim-based and PRISM-based Tw with SNODAS acting as the benchmark in the western United States. Parameter CTw is 0°C.
The performance of rain–snow partitioning is further investigated in six mountain ranges. Figure 11 shows the scatterplots between elevation and three contingency metrics of NN-based Tw. The differences between NN-, Gruber_TLR-, and PRISM-based Tw are also presented. HSS is not displayed because of its similar distribution with CSI. Metrics of NN-based Tw exhibit a clear relation with elevation. POD and FAR increase with decreasing elevation, particularly for the Cascade Range, Bighorn Mountain, Black Hills, and Uinta Mountains. The scatterplots of CSI have two stages in the Cascade Range, Bighorn Mountain, Uinta Mountains, and Sierra Nevada, showing a positive correlation with elevation at low elevation but negative correlation at high elevation. NN-based Tw acquires the best rain–snow partitioning results at around the average elevation, probably because ERA-Interim data approximate the temperature at the average elevation in the 0.75° grid pixel. Concerning CSI, Gruber_TLR and PRISM are better than NN at high and low elevations. However, Gruber_TLR and PRISM show worse performance than NN at midelevations in the Cascade Range and Sierra Nevada.
Scatterplots between elevation and (left) POD, (center) FAR, and (right) CSI for rain–snow partitioning in six mountains, that is, (from top to bottom) the Cascade Range, Bighorn Mountain, Black Hills, Uinta Mountains, Sierra Nevada, and Edwards Plateau. SNODAS serves as the comparison reference. Black circles represent metrics of NN-based Tw. Red circles represent the differences between metrics of Gruber_TLR- and NN-based Tw. Blue circles represent the difference between metrics of PRISM- and NN-based Tw. Black lines represent the average elevation of the six mountains.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Scatterplots between elevation and (left) POD, (center) FAR, and (right) CSI for rain–snow partitioning in six mountains, that is, (from top to bottom) the Cascade Range, Bighorn Mountain, Black Hills, Uinta Mountains, Sierra Nevada, and Edwards Plateau. SNODAS serves as the comparison reference. Black circles represent metrics of NN-based Tw. Red circles represent the differences between metrics of Gruber_TLR- and NN-based Tw. Blue circles represent the difference between metrics of PRISM- and NN-based Tw. Black lines represent the average elevation of the six mountains.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
Scatterplots between elevation and (left) POD, (center) FAR, and (right) CSI for rain–snow partitioning in six mountains, that is, (from top to bottom) the Cascade Range, Bighorn Mountain, Black Hills, Uinta Mountains, Sierra Nevada, and Edwards Plateau. SNODAS serves as the comparison reference. Black circles represent metrics of NN-based Tw. Red circles represent the differences between metrics of Gruber_TLR- and NN-based Tw. Blue circles represent the difference between metrics of PRISM- and NN-based Tw. Black lines represent the average elevation of the six mountains.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
On the whole, ground-based PRISM is the best because 1) the high resolution of PRISM enables better characterization of temperature, especially for mountains; 2) PRISM incorporates observations from a large number of meteorological stations; and 3) ground-based observations used by PRISM and SNODAS may overlap. Gruber_TLR-based Tw is only second to PRISM-based Tw. TLR-based downscaling methods are most effective in regions with drastic elevation and pressure variation where temperature tends to decrease linearly with increasing elevation.
d. Comparison with the current IMERG product
To prove the effectiveness of downscaled Tw, we compared the precipitation phase of the IMERG Final run product to the phase estimated by downscaled Tw in 2015. Only Gruber_TLR is used in this section because it is proved to be better than other methods in previous sections. IMERG products provide the probability of solid precipitation at the half hourly scale. To calculate the daily snow probability, we first calculated snowfall for each half hour by multiplying solid precipitation probability with total precipitation. Then, the daily snow probability is represented as the ratio between daily snowfall and daily total precipitation accumulated from half-hourly data. A threshold of 50% probability was selected as a rain–snow discriminator which corresponds to a Tw of 1.1°C over land (David Bolvin, IMERG Team, 2018, personal communication). Therefore, the CTw for rain–snow partitioning was also set to 1.1°C in this section. We also tested other CTw values and found the conclusions keep consistent.
Figure 12 shows the differences of contingency metrics between Gruber_TLR-based Tw and IMERG. The Gruber_TLR-based Tw is characterized by higher POD in the CONUS, particularly in the western United States, indicating that more snowfall events are captured compared to IMERG. Meanwhile, Gruber_TLR-based Tw falsely reported more snowfall events than IMERG with slightly higher FAR. On the whole, concerning CSI and HSS, which are more comprehensive than POD and FAR, Gruber_TLR-based Tw is generally better than IMERG, particularly for the western United States. For example, the CSI and HSS are 0.30 and 0.33 for IMERG Tw in the western United States, which are increased to 0.35 and 0.39 for Gruber_TLR-based Tw, respectively. Therefore, TLR-based downscaling methods contribute to better rain–snow partitioning, especially in complex terrain.
The differences of (a) POD, (b) FAR, (c) CSI, and (d) HSS between precipitation phase of Gruber_TLR-based Tw and IMERG in 2015. SNODAS is used as the snowfall reference.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
The differences of (a) POD, (b) FAR, (c) CSI, and (d) HSS between precipitation phase of Gruber_TLR-based Tw and IMERG in 2015. SNODAS is used as the snowfall reference.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
The differences of (a) POD, (b) FAR, (c) CSI, and (d) HSS between precipitation phase of Gruber_TLR-based Tw and IMERG in 2015. SNODAS is used as the snowfall reference.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-18-0041.1
5. Summary and concluding remarks
GPM IMERG uses temperature from reanalysis datasets such as ERA-Interim to separate rain and snow, while reanalysis data are produced at coarse resolutions necessitating the application of downscaling techniques. Purely statistical downscaling methods such as NN and BI (used in the current IMERG algorithm) cannot take the effect of topography on temperature into consideration. Therefore, the present study compared the performance of eight Ta downscaling methods in the CONUS with emphasis put on the western United States where the topography is complex and snowfall is frequent. Parameter Tw was calculated on the basis of downscaled Ta and Td and utilized to separate rain from snow. The performance of Tw-based rain–snow partitioning was evaluated and compared to IMERG using SNODAS as the benchmark.
Among the eight Ta downscaling methods, NN and BI showed similar performance with each other. The Ta based on NN and BI exhibited warm biases in high-altitude mountains but cold bias in low-altitude plains and valleys elevations. Gerlitz_regression greatly overestimated Ta in the CONUS and was worse than all the other methods. The other five TLR-based downscaling methods (FTLR, Gao_TLR, MA_TLR, Gruber_TLR, and PTLR) achieved better skill scores than NN and BI, particularly in mountainous areas. The error of NN and BI is notably reduced in high-altitude mountains such as the Cascade Range and Sierra Nevada. Among the eight downscaling methods, PTLR is the best since it utilized 4-km PRISM temperature data to calculate TLR. Other TLR-based methods only relied on the ERA-Interim temperature at different pressure levels and are globally applicable. Particularly, Gruber_TLR consistently outperformed other methods except for PTLR and is recommended in actual application.
To separate rain and snow, Tw was calculated based on downscaled Ta and RH. In the eastern United States, the eight downscaling methods acquired similar Tw with each other. However, in the western United States, the five TLR-based downscaling methods performed much better than NN and BI with much smaller MAE, ABIAS, and RMSE, and the improvement was particularly significant in high-altitude mountain ranges where snowfall is more frequent. For Tw between −2° and 2°C where precipitation phase usually changes, TLR-based methods are significantly better than NN and BI. On the whole, Gruber_TLR generates the best Tw.
The performance of rain–snow partitioning based on NN and Gruber_TLR Tw was evaluated in the western United States against SNODAS snowfall data. NN-based Tw overestimated (underestimated) the number of snowfall events in regions with low (high) elevation because NN cannot reflect temperature variation with elevation. Gruber_TLR-based Tw reduced the error of NN-based Tw, while PRISM-based Tw acquired the best rain–snow partitioning results since it employs ground-based temperature data. Further investigation in six typical mountains implied that the rain–snow partitioning metrics showed a clear relation with elevation, and Gruber_TLR and PRISM performed better than NN in high-altitude regions. Considering the outstanding performance of Gruber_TLR, we further compared the precipitation phase of IMERG to the phase estimated by Gruber_TLR-based Tw. Gruber_TLR is better at rain–snow partitioning compared to IMERG in CONUS with higher POD, CSI, and HSS, especially in the western United States.
In conclusion, TLR-based downscaling methods, particularly Gruber_TLR, can produce high-resolution Ta and Tw with more satisfactory quality than NN and BI, leading to better rain–snow partitioning. Although the study is conducted at the daily scale, we believe that the downscaling methods are also effective at the subdaily scale in global land and can be applied to the other products, for example, JMA used by IMERG Early and Late runs. However, the study still has some limitations. First, SNODAS snowfall data also contain uncertainties that are not quantified in this study and may have some effect on the evaluation of precipitation phase. Studies at regional scales with better ground-based snowfall observations are needed. Second, TLR-based downscaling methods cannot be applied over ocean where topographic information is absent. Fortunately, the temperature field is relatively even and the impact of snowfall is less significant over ocean. Finally, more efforts are needed to improve the effectiveness of TLR-based downscaling methods over relatively flat terrain and adjusting TLR values derived from reanalysis datasets according to topography characteristics.
Acknowledgments
This study was financially supported by the National Key Research and Development Program of China (2016YFE0102400), and the National Natural Science Foundation of China (Grants 71461010701, 91437214, and 91547210). A. Behrangi is supported by NASA Energy and Water Cycle Study(NNH13ZDA001N-NEWS) and NASA weather (NNH13ZDA001N–Weather) programs. Part of the research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Additional support came from a scholarship from the China Scholarship Council (CSC). Editors’ and reviewers’ comments for improving this manuscript are highly appreciated.
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