1JANUARY 2020 T A M A N G E T A L . 39

Linking Global Changes of Snowfall and Wet-Bulb Temperature

SAGAR K. TAMANG AND ARDESHIR M. EBTEHAJ Saint Anthony Falls Laboratory and Department of Civil, Environmental and Geo-Engineering, University of Minnesota–Twin Cities, Minneapolis, Minnesota

ANDREAS F. PREIN AND ANDREW J. HEYMSFIELD National Center for Atmospheric Research, Boulder, Colorado

(Manuscript received 4 April 2019, in final form 20 August 2019)

ABSTRACT

Snowfall is one of the primary drivers of the global cryosphere and is declining in many regions of the world with widespread hydrological and ecological consequences. Previous studies have shown that the probability of snowfall occurrence is well described by wet-bulb temperatures below 18C (1.18C) over land (ocean). Using this relationship, wet-bulb temperatures from three reanalysis products as well as multisatellite and reanalysis precipitation data are analyzed from 1979 to 2017 to study changes in potential snowfall areas, snowfall-to- rainfall transition latitude, snowfall amount, and snowfall-to-precipitation ratio (SPR). Results are presented at hemispheric scales, as well as for three Köppen–Geiger climate classes and four major mountainous regions including the Alps, the western United States, High Mountain Asia (HMA), and the Andes. In all reanalysis products, while changes in the wet-bulb temperature over the Southern Hemisphere are mostly insignificant, significant positive trends are observed over the Northern Hemisphere (NH). Significant reductions are 2 observed in annual-mean potential snowfall areas over NH land (ocean) by 0.52 (0.34) million km2 decade 1 2 due to an increase of 0.348C (0.358C) decade 1 in wet-bulb temperature. The fastest retreat in NH transition 2 latitudes is observed over Europe and central Asia at 0.78 and 0.458 decade 1. Among mountainous regions, 2 the largest decline in potential snowfall areas is observed over the Alps at 3.64% decade 1 followed by the 2 western United States at 2.81% and HMA at 1.85% decade 1. This maximum decrease over the Alps is 2 2 associated with significant reductions in annual snowfall of 20 mm decade 1 and SPR of 2% decade 1.

1. Introduction et al. 2008; Ashfaq et al. 2013; Marty et al. 2017; Mote et al. 2018). Snow and its meltwater play a crucial role in the global Snowfall accumulation controls the mass balance of water and energy cycle. Snowpack stores freshwater in snowpack and glaciers. The changes of snowfall are winter and releases it during the summer when it is largely due to competing effects of changes in pre- needed the most (Viviroli et al. 2007; Wan et al. 2014). cipitation, air temperature, and moisture content. In- In a warmer world, a lower proportion of winter pre- creased global temperature and specific humidity are cipitation falls as snow and winter snowpack melts ear- expected to alter the spatial distribution and intensity of lier in spring, causing water shortages in summer global precipitation (Willett et al. 2007). As the air (Barnett et al. 2005). Climate projections indicate that a temperature increases, the water holding capacity of air population of almost 2 billion people could be exposed also increases, which could give rise to more pre- to a high risk of decreased snow water supply in the next cipitation. However, the snowfall-to-precipitation ratio century (Mankin et al. 2015). Multidecadal observations might decrease, especially over areas where the air show that snow-cover areal extent has declined signifi- temperature changes seasonally around the freezing cantly over the Northern Hemisphere (NH) (Brown and point. Regional studies report that the snowfall is de- Robinson 2011; Hori et al. 2017). There are also regional creasing over important mountainous regions of the studies indicating declines of important snowpack res- world, including the Himalayas (Gusain et al. 2014; Mir ervoirs around the globe at different rates (Rauscher et al. 2015), the Tibetan Plateau (Wang et al. 2016), the Italian Alps (Valt and Paola 2013), the Rockies and Corresponding author: Sagar K. Tamang, [email protected] Sierra Nevada (Howat and Tulaczyk 2005; Knowles

DOI: 10.1175/JCLI-D-19-0254.1 Ó 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 40 JOURNAL OF CLIMATE VOLUME 33 et al. 2006; Feng and Hu 2007), and the Tian Shan (Guo below saturation and air temperatures between 0.68 and and Li 2015). It is also reported that over the Arctic, 3.48C. snowfall has declined, largely due to decreasing total The objective of this paper is to enhance our un- precipitation and increasing lower-atmospheric tem- derstanding of the global changes in potential snowfall perature (Screen and Simmonds 2012). areas, the position of the rainfall-to-snowfall transition Despite significant progress in the understanding of latitudes, total snowfall amount (defined as snow water regional changes in snowfall, there is still a large gap in equivalent), and the snowfall-to-precipitation ratio (SPR) our knowledge about the global changes in snowfall in the past few decades. The paper focuses on changes space–time distribution. Satellite precipitation data are over the Köppen–Geiger (Peel et al. 2007)Aridcold, promising to help close this gap in cold climate regions, cold, and polar climate classes as well as four important which typically have sparse ground observations. How- mountainous regions of the world: the Alps, the western ever, unlike rainfall (Bolvin et al. 2009; Huffman et al. United States including the Rockies and Sierra Nevada, 2009; Behrangi et al. 2016), a sufficiently long and reli- High Mountain Asia (HMA), and the Andes. For the able record of satellite snowfall is still lacking. The re- analyses, we use observational and reanalysis precipi- cently launched Global Precipitation Measurement tation estimates and 2-m wet-bulb temperature pro- (GPM; 2014–present) satellite (Hou et al. 2014; cessed from multiple reanalysis datasets. To improve the Skofronick-Jackson et al. 2017) will reduce this gap over inference, reanalysis data of wet-bulb temperatures are the years to come, but its observation record is still too merged and the computed SPR values are validated, us- short. Multisensor precipitation products such as the ing the wet-bulb temperature and SPR derived from Tropical Rainfall Measurement Mission (TRMM) ground-based gauge observations by the National Cli- Multi-Satellite Precipitation Analysis (TMPA; Huffman matic Data Center [NCDC; now known as the National and Bolvin 2013) and Pentad Global Precipitation Cli- Centers for Environmental Information (NCEI)]. matology Project (GPCP) (Xie et al. 2003) provide The paper is organized as follows: Section 2 discusses records of cumulative precipitation obtained from a the datasets and preprocessing tasks. The key measure combination of rain gauges and retrievals from a se- of changes and a summary of the used statistical ap- ries of spaceborne sensors. However, these products proaches for trend identification are described in section 3. currently do not have any specific information on pre- Section 4 demonstrates and interprets the results while cipitation phase. section 5 concludes and discusses findings and its impli- The phase of precipitation can be inferred from the cations. Computation of the wet-bulb temperature using near-surface air temperature (Kienzle 2008; Dai 2008), the approach by Stull (2016), statistical trend analysis, and dewpoint temperature (Marks et al. 2013), or wet-bulb the quality metrics used in the validation parts are ex- temperature (Ding et al. 2014; Sims and Liu 2015; plained in the appendixes. Zhong et al. 2018). The energy budget of falling hy- drometeors is affected by atmospheric humidity (Harpold et al. 2017) and thus the wet-bulb temperature, which 2. Data and preprocessing accounts for the effects of the air moisture content, a. Wet-bulb temperature can better capture the phase of precipitation than the air temperature (Harder and Pomeroy 2013; Ding We use the latest generation of three reanalysis et al. 2014). Sims and Liu (2015) studied the un- products, from credible meteorological agencies in certainty range defined as the difference between the Europe, Asia, and the United States, to process and 10th and 90th percentiles of the snowfall conditional characterize the global changes of the wet-bulb tem- probability using 9700 stations over global land and perature. These reanalysis products include the Euro- oceans from 1950 to 2007. They found that the un- pean Centre for Medium-Range Weather Forecasts certainty range is narrower for the wet-bulb temper- (ECMWF) interim reanalysis (ERA-Interim) (Dee ature than the air temperature both over land (2.58 vs et al. 2011), the Japanese 55-yr Reanalysis (JRA-55) 3.38C) and oceans (3.68 vs 5.08C). Their results show (Kobayashi et al. 2015), and the NCEP–DOE R-2 that precipitation is in solid form with more than 50% (Kanamitsu et al. 2002) by the United States National probability when the near-surface wet-bulb tempera- Centers for Environmental Prediction (NCEP) and ture is below 18C over land and 1.18C over oceans. Department of Energy (DOE). These reanalysis prod- More recently, Jennings et al. (2018) also showed ucts provide the required information for calculating improved precipitation phase detection by the methods wet-bulb temperature from 1979 to the present every that incorporate air humidity than those solely relying 6 h, at spatial grid resolutions of 0.1258, 0.56258, and 2.58, on air temperature, particularly at a relative humidity respectively. 1JANUARY 2020 T A M A N G E T A L . 41 b. Precipitation c. Gauge data

Uncertainty in global estimates of precipitation can be We used gauge data (2011–15) from the NCDC large, particularly in regions with low station density Global Surface Summary of the Day (GSOD; Lott and snow-dominated environments (Sun et al. 2018). 1998; Smith et al. 2011) for error analysis of the wet-bulb Satellite-based precipitation datasets are expected to temperatures and validation of SPR. Gauge observa- provide improved estimates of the global precipitation tions of air temperature, dewpoint temperature, pres- and enhance the accuracy of the reanalysis products. sure, precipitation amount, and indicator of its type (fog, However, passive microwave satellite data are not free rain, snow, or hail) were obtained for calculating the of error, especially over complex topography where wet-bulb temperature and SPR. 3579 NCDC stations ; the microwave signal of shallow precipitation is weak with 4.1 million station days (data from one station in (Ebtehaj et al. 2016). For example, intercomparison one day) were used (Fig. 1), while only 803 station years studies over Europe have shown that satellite products could be utilized for annual validation of the SPR. The 21 have a tendency to overestimate precipitation over flat reason is that all stations with more than 10 days yr of regions and underestimate it over mountainous regions missing information on precipitation amount and phase (Prein and Gobiet 2017). Sun et al. (2018) compared were not utilized. Furthermore, to avoid any inflation of annual precipitation estimates from multiple sources validation statistics due to lower SPR values, any station , with 70 000 gauge station data obtained from the Global years with 0.01 SPR values were removed. It should be Precipitation Climatology Center (GPCC). It is shown noted that NCDC data are among a large suite of sat- that gauge-corrected satellite estimates of precipitation ellite and ground-based observations that are assimi- such as GPCP perform better than the reanalysis products lated into the used reanalysis products and merged into such as ERA-Interim, JRA-55, and NCEP–DOE R-2. the GPCP data. However, due to model and represen- Here we use a multisensor observational precipitation tative errors and the differences between the used data dataset in combination with reanalysis precipitation assimilation techniques, this does not necessarily imply from the ERA-Interim to estimate the robustness of our that the reanalysis errors with respect to the gauge data results. are zero or strongly correlated. For observational precipitation data, we use the Pentad GPCP, version 2.2, which provides multisensor 3. Methodology estimates of 5-day surface global precipitation at a spatial resolution of 2.58 from 1979 to 2016 (Xie et al. a. Reanalysis ensemble mean 2003, 2011). This product is created by merging the Multiple reanalysis data can be considered as an en- Pentad Climate Prediction Center (CPC) Merged semble realization of the underlying variable of interest Analysis of Precipitation (CMAP) (Xie and Arkin and can be integrated for reducing the uncertainty of 1997) and the GPCP monthly multisensor precipitation inference (Hagedorn et al. 2005; Solman and Orlanski product (Adler et al. 2003). The Pentad CMAP data- 2016). In this study, we use the maximum likelihood set optimally combines gauge precipitation data from (ML) estimator of the reanalysis products. To that end, more than 6000 Global Telecommunication System we assume that the 2-m wet-bulb temperature Tt,m by (GTS) stations, NCEP–NCAR reanalysis precipitation wb reanalysis product m at time t is related to the ground (Kalnay et al. 1996), and precipitation estimates from truth wet-bulb temperature Tt as follows: the infrared sensor on board the Geostationary Oper- wb ational Environmental Satellite (GOES), the Micro- Tt,m 5 Tt 1 « , « ; N (0, s2 ), (1) wave Sounding Unit on the Television Infrared wb wb m m m Observation Satellite (TIROS), the Special Sensor where the reanalysis error «m are uncorrelated zero- Microwave Imager (SSM/I) on board the Defense mean normally distributed random variables with variance Meteorological Satellite Program (DMSP) satellites, s2 m. Therefore, the likelihood function can be obtained as and the Advanced Very High Resolution Radiometer L t,m t }P3 2 t,m 2 t 2 s2 (Twb jTwb) m51 exp[ (Twb Twb) /2 m]forwhich (AVHRR) on board the National Oceanic and Atmo- ^t the ML estimate of the reanalysis wet-bulb temperature Twb spheric Administration (NOAA) operational sun- is as follows: synchronous polar-orbiting satellites. In accordance to 3 (Tt,m 2 Tt )2 the GPCP policy of avoiding numerical model influence, T^t 5 arg min å wb wb , (2) wb s2 the observation-only version of the Pentad CMAP Tt m51 wb m (CMAP/O) was utilized in the production of Pentad GPCP. which can be simplified as 42 JOURNAL OF CLIMATE VOLUME 33

FIG. 1. (a) Location of the NCDC gauge stations used in the study for error analysis of the reanalysis-based wet- bulb temperature and validation of SPR from 2011 to 2015. The map shows three Köppen–Geiger climate classes including the arid cold (orange), cold (yellow), and polar (blue). Also shown are the elevation maps, from the NOAA digital elevation model at 1-km resolution, which determine the boundaries for the mountainous regions of (b) the western United States, (c) the Alps, (d) HMA, and (e) the Andes (Blyth et al. 2002).

3 set. Throughout, we use daily wet-bulb temperature ^t 5 å t,m Twb wmTwb , (3) from reanalysis datasets and their ensemble mean to first m51 compute daily potential snowfall area and then infer its 2 5 s22 s22 1 seasonal and annual changes. where wm m åm m and the variance of the 21 ML estimator is given by å s22 . Because of the m m c. Snowfall-to-rainfall transition latitudes Gaussian assumption, the ML estimate is equivalent to an ensemble mean that is weighted based on the inverse The analysis of the potential snowfall areas provides a of the error variance of each reanalysis product. In the bulk quantitative indication on how areal extent of above formalism, we assumed that the reanalysis data global snowfall is shrinking or expanding over time. are unbiased, which is a reasonable assumption as will be However, another key question is this: Where, and to shown later. what extent, is the global snowfall changing into rain- fall? The location and movement of the boundary of b. Potential snowfall area potential snowfall areas capture the regions that are Denoting the wet-bulb temperature at a pixel-level experiencing the most significant interannual variability

(i, j)asTwb(i, j), the potential snowfall area is defined as of snowpack water storage and related hydrologic re- the interior area of the set S of all global pixels over sponse. As explained before, this freezing boundary ›S , # s s s which Twb(i, j) Twb. Here, Twb denotes snowfall can be defined as the contour of Twb that separates threshold of 18C over land and 1.18C over oceans (Sims potential snowfall and rainfall areas. To that end, we and Liu 2015), which defines the boundaries ›S of the define the snowfall-to-rainfall transition latitudes as the 1JANUARY 2020 T A M A N G E T A L . 43 boundary of the potential snowfall areas with a pre- trends. The Theil–Sen method computes the trend by specified decadal exceedance probability. For example, taking the median of the slopes of all possible lines that latitudes with 25% exceedance probability represent the are fitted to pairs of sample points. This method does not boundary of the areas within which the snow can fall at require any parametric assumption about the probabil- least 25% of the days over a decade. This decadal rep- ity distribution of the samples and exhibits higher degree resentation is used to capture the long-term trends and of accuracy than the ordinary least squares (OLS), in the cancel out the short-term interannual variabilities. presence of heteroscedasticity (Wilcox 2010). Addi- tionally, since this approach relies on the median of the d. Total snowfall and snowfall-to-precipitation ratio slopes, the estimated trends are more robust to obser- As previously noted, we also study the changes of total vational outliers than the OLS, which approximates snowfall and snowfall-to-precipitation ratio (SPR) not the mean value of the trends (Matousek et al. 1998; only for the Pentad GPCP but also for ERA-Interim. Wilcox 2010). We combine the ensemble-mean reanalysis wet-bulb Numerous tests have been examined to quantify the temperature with the Pentad GPCP precipitation to statistical significance of the Theil–Sen estimator such as compute the SPR. To that end, the ensemble mean of the parametric t test (Student 1908) and nonparametric reanalysis wet-bulb temperatures is computed daily at Mann–Kendall (MK) test (Mann 1945; Kendall 1948). the spatial resolution of ERA-Interim, that is, 0.1258; Here we adopt the bootstrap MK test (BS-MK; Douglas however, cumulative Pentad GPCP precipitation is et al. 2000)asYue and Pilon (2004) showed that this available every 5 days at a spatial resolution of 2.58. method has a higher probability of correct rejection of Therefore, the Pentad GPCP data are first mapped onto the null hypothesis for linear trend detection of non- the grids of the ensemble mean through the nearest- Gaussian data structure, among other commonly neighbor interpolation to avoid any loss or addition of used tests. spurious information. The relative frequency of snowfall The asymptotic null distribution of the MK test sta- occurrence for each pixel is defined as a fraction of the tistic is valid under the assumption of serial in- number of days when the daily wet-bulb temperature is dependence (von Storch 1995). To formally account for below the snowfall threshold in 5 days. The computed the effects of serial dependence, prewhitening (von relative frequency is then multiplied with precipitation Storch 1995) and trend-free prewhitening (Yue et al. amount to obtain an estimate of snowfall amount. An- 2002) approaches have been proposed. Yue and Wang nual SPR is finally obtained by dividing the cumulative (2004) showed that the presence of positive (negative) snowfall amount by the annual cumulative precipitation serial correlation in the data inflates (deflates) the var- amount as follows: iance of MK test statistic and thus proposed a variance- n p correction method. Additionally, block bootstrap å t fs (i, j)P(i, j) approaches (Kundzewicz and Robson 2000; Önöz and 5 SPR(i, j) 5 t 1 , (4) Bayazit 2012) have been suggested to approximate P(i, j) directly the null distribution of the MK test statistic where the relative frequency of snowfall occurrence is through resampling, without removing the serial de- t 5 T t t fs (i, j) (1/T)åt511S [Twb(i, j)], 1S [Twb(i, j)] is an in- pendence of the data. Khaliq et al. (2009) compared the t # s dicator function that is equal to 1 if Twb(i, j) Twb and 0 performance of the explained methods and found that otherwise, P(i, j) represents the pixel-level cumulative the prewhitening methods are conservative in identify- precipitation during the Pentad GPCP temporal reso- ing significant trends while both variance correction and lution, T 5 5 denotes the number of days in a pentad block bootstrap methods perform well for dependent period, and np is the number of 5-day precipitation data time series. points per year. The variants of the block bootstrap method (Kunsch Precipitation and snowfall from the ERA-Interim are 1989; Carlstein 1986; Kunsch 1989; Liu and Singh 1992; obtained from the 12-hourly accumulated totals. The values Politis and Romano 1994) are an extension to the orig- arethensummedupfortheentireyeartoprovidethean- inal bootstrap inference approach (Efron 1979) for ap- nual precipitation and snowfall as the snow water equiva- proximating the sample distribution of a statistic in lent. Then the annual SPR is finally obtained by dividing the serially dependent datasets. This method reconstructs annual snowfall by the annual precipitation amount. the bootstrap samples through resampling of data blocks beyond which the dependent structure of the data be- e. Trend analysis comes negligible. Here, we confine our consideration to We use the nonparametric Theil–Sen method (Theil the classic moving-block bootstrap (MBB; Liu and 1950; Sen 1968) for computing the magnitude of linear Singh 1992), which has been applied and tested 44 JOURNAL OF CLIMATE VOLUME 33

FIG. 2. (left) Trends of annual-mean wet-bulb temperature and (right) its zonal mean for the reanalysis products from 1979 to 2017. successfully for significance analysis of the MK esti- Then, we present the spatial trends in the mean en- mates of linear trends (Khaliq et al. 2009; Önöz and semble wet-bulb temperature over the areas where the Bayazit 2012). majority of the reanalysis products (i.e., 2 out of 3) Throughout, the trends at significance level a are re- agree. Focusing on the ensemble mean, the changes of ported as ba(bmin 2 bmax), where ba denotes the trend the potential snowfall areas, transition latitudes, total of the ensemble mean and values in parentheses denote snowfall, and snowfall-to-precipitation ratios are quan- the minimum and maximum of trends by the three re- tified and discussed. analysis products. The reported changes without a sub- a. Changes in wet-bulb temperature script are insignificant at a 5 0.05. Figure 2 shows the trends in annual-mean wet-bulb temperature (left) and its zonal mean (right) during the 4. Results study period. Over the NH, there is a good agreement In this section we present the results on changes of the between the three datasets, especially with respect to the wet-bulb temperatures among all reanalysis products detected positive trends over cold and polar climate and highlight their areas of discrepancy and agreement. regimes above the Arctic Circle. In particular, large 1JANUARY 2020 T A M A N G E T A L . 45

FIG. 3. Probability histogram of error in wet-bulb temperatures from (a) ERA-Interim, (b) JRA-55, and (c) NCEP–DOE R-2 as well as (d) the scatter density plot of their ensemble mean vs the NCDC GSOD gauge stations. The errors are computed by comparing the reanalysis and gauge station data from 2011 to 2015. areas of Canada’s tundra and boreal forests, the U.S. are almost unbiased with respect to the areas that are Midwest, the Greenland Ice Sheet, northern Europe, densely populated by the gauges. Fitted Gaussian dis- the central Siberian Plateau, and the Scandinavian tributions have standard deviations of 1.478, 1.58, and peninsula have experienced a warming trend above 2.698C for ERA-Interim, JRA-55, and NCEP–DOE R-2, 2 0.38C decade 1. Some disagreements between the re- respectively. As shown in Fig. 3d, the ensemble-mean analysis products can be observed in lower latitudes, wet-bulb temperature compares well with the gauge data especially over the Iranian Plateau, Indian peninsula, as the coefficient of determination R2 reaches 0.98 and and East Asia, where only ERA-Interim and JRA-55 the ensemble-error standard deviation is reduced to indicate a coherent warming trend. The disagreement is 1.468C. more apparent over western Africa and across the North To better understand the spatial pattern of the trends, Atlantic Ocean, where only NCEP–DOE R-2 shows a binary masks of significant warming and cooling trends coherent warming trend. Over higher latitudes (708– (a 5 0.05) and insignificant trends are created for each 908N), zonal-mean trends are consistently positive and reanalysis product and then overlaid (Fig. 4a) to identify 2 larger than 0.58C decade 1 in all three reanalysis prod- the areas of agreement. The trend of the annual ensemble- ucts (Fig. 2, right column). mean wet-bulb temperatures is computed and mapped Over the SH, there is large disagreement between the onto the ERA-Interim 0.1258 grid, using nearest-neighbor reanalysis datasets. The NCEP–DOE R-2 data indicate interpolation, over the areas with majority agreement that the annual-mean wet-bulb temperature is de- (Fig. 4b). creasing coherently over the Andes and increasing over Over the NH lands, in all reanalysis products, positive Australia, whereas these trends are not apparent in trends are observed over the Arctic, the Midwest and other reanalysis products. The disagreement is most northeastern United States, the European continent pronounced over Antarctica where ERA-Interim does except the Iberian Peninsula, western Eurasia, the Ti- not show any spatially organized trend while a positive betan highlands, and western China. The trends are 2 trend is seen in the other datasets, especially in NCEP– around 0.88C decade 1 over the Arctic and reduce to 2 DOE R-2. This warming trend is more significant and less than 0.48C decade 1 over the midlatitudes and 2 reaches more than 0.68C decade 1 over Antarctica subtropical zones. Over the SH lands, areas of positive with a peak of around 0.858C around 808S. trends are less coherent. The majority of positive trends agree only over parts of Antarctica. Significant trends b. Ensemble-mean wet-bulb temperature are observed over the Queen Maud Land and coasts of the As previously explained, we use ground-based gauge Ross Dependency. It is important to note that the positive 2 stations from 2011 to 2015 to compute the ensemble- trends above 0.48C decade 1 are concentrated over the mean wet-bulb temperature and validate some of the Filchner, the Fimbulisen, and the Ross Ice Shelves. results. The error distribution of the reanalysis wet-bulb The results in Fig. 4c indicate that the changes are temperatures is shown in Figs. 3a–c. The reanalysis data significant for all climate regimes except over the SH 46 JOURNAL OF CLIMATE VOLUME 33

FIG. 4. (a) Spatial distribution of the agreement in significant trends (a 5 0.05) in the wet-bulb temperature between the three reanalysis products, (b) spatial distribution of the trends, and (c) the ensemble mean over the Köppen–Geiger climate classes and four mountain regions. In (c), significant trends are labeled by an asterisk. The trends are also shown in a polar projection system over (d) the Arctic and (e) Antarctica.

arid cold climates. Specifically, the ensemble mean shows Figure 5 shows the time series of the NH and SH 21 thehighestwarmingrateof0.690.05 (0.66–0.69)8C decade annual-mean wet-bulb temperatures over global land (where the subscript indicates the statistical sig- and oceans, while Table 1 reports the seasonal changes nificance level) over the NH polar climate regime, fol- as well. All reanalysis products agree over the NH both lowed by NH areas with cold and arid cold climates at in terms of the trends and their annual-mean values, 21 0.390.01 (0.36–0.41)8C decade and 0.200.01 (0.11–0.24)8C whereas over the SH the results show large un- 2 decade 1, respectively. The majority of the reanalysis certainties. The highest mean wet-bulb temperature is products indicate that there has been a warming trend observed in 2016 over the NH, both over land and over the studied mountainous regions, among which oceans among all reanalysis products, whereas there is the Alps are experiencing the highest positive trend not such an agreement in SH. Trend analysis suggests 21 at 0.270.01 (20.09–0.35)8C decade followed by the that the NH annual ensemble-mean wet-bulb tempera- HMA and the western United States at 0.240.01 (0.21– ture is rising over land and oceans at 0.340.01 (0.32– 21 21 21 21 0.27)8C decade and 0.180.05 (0.10–0.29)8C decade , 0.35)8C decade and 0.350.01 (0.34–0.41)8Cdecade . respectively. Among all seasons, highest warming is observed during 1JANUARY 2020 T A M A N G E T A L . 47

FIG. 5. Time series of annual-mean wet-bulb temperature for (a) NH land, (b) NH oceans, (c) SH land, and (d) SH oceans from 1979 to 2017 for the three reanalysis products and their ensemble mean. Here, ba represents the 2 trend value of the ensemble-mean wet-bulb temperature (8C decade 1) at significance level a. Trend values without a subscript are insignificant.

21 21 21 the fall both over land at 0.370.05 (0.35–0.38)8C decade 0.41)8C decade and 0.03 (20.02 to 0.16)8Cdecade 21 and oceans at 0.490.05 (0.44–0.61)8Cdecade (see over land and oceans, respectively. The SH spring man- Table 1). ifests the highest warming rates over both over land and 21 Similar to the NH, annual-mean wet-bulb temperature oceans with the rate of 0.260.01 (0.15–0.56)8Cdecade 21 over the SH is rising, but at a lower rate of 0.130.01 (0.04– and 0.070.01 (0.04–0.21)8C decade .

TABLE 1. Annual and seasonal changes of the hemispheric-mean wet-bulb temperature over the land and oceans. We define four seasons as winter (December–February), spring (March–May), summer (June–August), and fall (September–November) for the NH and winter (June–August), spring (September–November), summer (December–February), and fall (March–May) for the SH. Due to the absence of information during December 1978, the data over the NH winter (SH summer) were not analyzed in that year. The boldface values are significant at a 5 0.05.

ERA-Interim JRA-55 NCEP–DOE R-2 Ensemble Seasons Land Ocean Land Ocean Land Ocean Land Ocean Northern Annual 10.33 10.35 10.35 10.34 10.32 10.41 10.34 10.35 Winter 10.23 10.51 10.26 10.44 10.24 10.49 10.25 10.47 Spring 10.37 10.37 10.37 10.32 10.36 10.38 10.37 10.36 Summer 10.25 10.12 10.28 10.14 10.24 10.16 10.26 10.14 Fall 10.38 10.44 10.37 10.49 10.35 10.61 10.37 10.49 Southern Annual 10.04 20.02 10.15 10.03 10.41 20.16 10.13 10.03 Winter 10.01 10.02 10.15 10.03 10.53 10.31 10.12 10.07 Spring 10.15 10.04 10.29 10.06 10.56 10.21 10.26 10.07 Summer 20.06 20.04 10.14 10.05 10.13 20.04 10.06 10.00 Fall 10.01 20.06 10.11 20.02 10.33 10.17 10.09 20.01 48 JOURNAL OF CLIMATE VOLUME 33

FIG. 6. Time series of the annual-mean potential snowfall areas for (a) NH land, (b) NH oceans, (c) SH land, and (d) SH oceans from 1979 to 2017 for the three reanalysis products and their ensemble mean. The values of ba 2 represent the trend of the ensemble mean (million km2 decade 1) at significance level a 5 0.05 and the values without subscript are insignificant. c. Changes in potential snowfall areas The contrasting nature of changes of potential SH snowfall areas and mean wet-bulb temperature exists The annual time series of the hemispheric-mean po- due to the spatial heterogeneity of the temperature tential snowfall areas are shown in Fig. 6 and the sea- trend. Figure 4b shows that the positive trend in mean sonal values are reported in Table 2 as well. Over the wet-bulb temperature is largely due to warming of the NH land, annual-mean potential snowfall areas are de- subtropical regions in the southern Pacific, Atlantic, and 2 21 creasing at a rate of 0.520.01 (0.44–0.56) million km decade , Indian Oceans with no effect on the potential snow- which is more than over NH oceans: 0.340.01 (0.28–0.39) fall areas. Because the temperature is well above the 2 million km2 decade 1. Seasonal analysis suggests that the snowfall threshold throughout the year. In fact, the in- shrinkage rate is largest during the NH spring at 0.810.01 crease of SH potential snowfall areas has occurred over 2 21 (0.58–0.86) million km decade and fall at 0.440.01 (0.41– the Southern Oceans within temperate and Arctic cli- 2 0.58) million km2 decade 1 over the land and oceans, mate zones, where the mean wet-bulb temperature is respectively. decreasing. However, the results over the SH are different. Over Annual-mean potential snowfall areas are de- land, no significant reduction in annual-mean poten- creasing over all studied Köppen–Geiger climate clas- tial snowfall area is observed, whereas over oceans it ses and the four mountain regions. Among the three has increased significantly at the rate of 0.320.01 (0.03– climate classes, the highest decrease is observed over 2 21 0.53) million km decade —despite a detected in- the NH cold climate regime at the rate of 0.330.05 (0.25– 2 crease in the mean wet-bulb temperature (Fig. 5). No 0.34) million km2 decade 1 followed by the polar and significant seasonal changes are detected over the SH the arid cold climates at the rate of 0.060.05 (0.06–0.07) 2 21 land (Table 2) whereas over the oceans all seasonal million km decade and 0.050.01 (0.03–0.06) million 2 changes are significant, except winter. The highest km2 decade 1, respectively. On average, we have lost 0.02 2 21 shrinkage rate occurs during the summer at 0.550.01 million km decade of snowfall areas over the four 2 (0.31–0.70) million km2 decade 1. mountainous regions. The largest decrease is observed 1JANUARY 2020 T A M A N G E T A L . 49

2 21 TABLE 2. Annual and seasonal changes of hemispheric-mean potential snowfall areas (million km decade ). The values in parentheses represent percentage of changes per decade with respect to the mean values. The boldface values are significant at a 5 0.05.

ERA-Interim JRA-55 NCEP–DOE R-2 Ensemble Seasons Land Ocean Land Ocean Land Ocean Land Ocean Northern Annual 20.53 20.28 20.56 20.39 20.44 20.35 20.52 20.34 (21.81) (21.61) (21.89) (22.35) (21.43) (22.04) (21.78) (21.99) Winter 20.31 20.36 20.34 20.48 20.14 20.43 20.30 20.42 (20.59) (21.41) (20.64) (21.93) (20.26) (21.75) (20.56) (21.67) Spring 20.79 20.04 20.86 20.21 20.58 20.04 20.81 20.10 (22.49) (20.19) (22.65) (21.03) (21.67) (20.21) (22.52) (20.49) Summer 20.30 20.23 20.34 20.48 20.49 20.35 20.32 20.34 (27.92) (23.10) (28.44) (26.42) (28.65) (23.56) (28.09) (24.36) Fall 20.71 20.41 20.78 20.46 20.37 20.58 20.70 20.44 (22.49) (22.81) (22.68) (23.30) (21.29) (24.04) (22.44) (23.10) Southern Annual 20.01 10.53 20.02 10.16 10.04 10.03 20.01 10.32 (20.07) (11.61) (20.18) (10.50) (10.33) (10.11) (20.06) (11.03) Winter 20.01 10.38 20.02 10.07 10.05 20.28 20.01 10.16 (20.11) (10.99) (20.19) (10.18) (10.37) (20.84) (20.10) (10.44) Spring 20.01 10.34 20.02 10.17 10.03 20.06 20.01 10.26 (20.10) (10.91) (20.14) (10.48) (10.22) (20.19) (20.08) (10.72) Summer 20.01 10.70 20.01 10.31 10.01 10.57 20.00 10.55 (20.04) (12.66) (20.13) (11.23) (10.12) (12.53) (20.01) (12.18) Fall 20.02 10.58 20.02 10.14 10.06 20.07 20.01 10.31 (20.14) (11.95) (20.21) (10.49) (10.48) (20.28) (20.08) (11.08)

over the HMA at 0.050.01 (0.04–0.06) million Focusing on the NH terrestrial changes, among those 2 km2 decade 1 followed by the western United regions where at least 25% of the time the snowfall oc-

States and Andes at the rate of 0.010.05 (0.00–0.02) currence is likely, eastern and southeastern Europe, the 2 21 million km decade and 0.010.05 (20.03–0.02) Middle East, and some regions south of central Asia have 2 million km2 decade 1. It is important to note that experienced significant shrinkage. From west to east, the the highest percentage reduction is observed over the changes extend from lowlands in Poland to the Baltic Sea, 21 Alps at 3.640.01 (27.54–4.84)% decade followed by southwestern Russia, southern Kazakhstan, and the Aral the western United States and HMA with reduction Sea. Over southeastern Europe, Serbia, Bulgaria, and 21 of 2.810.05 (1.91–3.27)% decade and 1.850.05 (1.53– Romania have been experiencing shrinkage of snowfall 2 2.18)% decade 1, respectively. To understand where area. In the Middle East, the changes are detected over these changes have occurred, the daily ensemble-mean the central west portion of Turkey and the foothills of the wet-bulb temperature was used to compute the per-pixel Alborz and Zagros mountain ranges in the Iranian Pla- annual exceedance probability of potential snowfall oc- teau. The areas that are likely to receive snowfall more currence. To that end, we created daily binary masks over than 50% of the time are shrinking mostly over North the areas where the wet-bulb temperatures are below the America’s Rocky Mountains, Canada’s boreal forests, snowfall thresholds. Then, annual binary masks of po- northwest Russia, and southwest Scandinavia, especially tential snowfall occurrence are produced to delineate the over Finland and Sweden. The shrinkage areas, with at areas over which the potential snowfall occurs at least least 75% of snowfall occurrence, are over the southern 25%, 50%, and 75% of days in a year. Then a pixel-level Himalayan range of HMA, eastern parts of the Tibetan frequency value is obtained by summing the annual bi- Plateau, and northern Siberia. Over North America, nary masks over the entire 39 years of data (Figs. 7a–f). much of the shrinkage is observed over the Brooks For example, when an area shows a frequency value of 10 mountain range in Alaska and Canadian barren grounds. for the 25% exceedance probability, it means that for 10 d. Changes in transition latitudes years the area could potentially receive snowfall at least 25% of the days in a year. Thus, when the frequency In this section we confine our considerations only to values are decreasing poleward it implies that the po- the NH for characterizing the changes on the boundary tential snowfall areas, at different annual exceedance of the potential snowfall areas. As previously noted, the levels, are shrinking. motivation is to understand where and to what extent 50 JOURNAL OF CLIMATE VOLUME 33

FIG. 7. Hemispheric maps showing areas over which annual frequency of potential snowfall occurrence have changed during the last four decades. Results are shown for exceedance probabilities of (left) 25%, (center) 50%, and (right) 75% in the (a)–(c) NH and (d)–(f) SH.

the snowfall-to-rainfall transition latitudes are moving. To (Fig. 8d). Isolated islands of changes are formed over that end, the boundary of the potential snowfall areas, the western United States and HMA (Figs. 8d,g). Be- with a decadal exceedance probability of 25%, 50%, and cause of the steepness of the mountainous areas, 75%, are quantified. For example, the latitudes with 25% changes of areal extent are small and rates should be exceedance probability represent the boundary of the areas further studied as a function of elevation. Over Europe within which snowfall occurrence is probable at least 25% and central Asia, a significant northward retreat is of the days within a decade. This decadal representation is observed over the Norwegian Sea, eastern Russia, and used to capture the long-term trends over a window of time northern Kazakhstan (Fig. 8g). For the 75% level, and cancel out the short-term interannual variability. transition latitudes are markedly retracting over The transition latitudes with exceedance probability northern Quebec in Canada (Fig. 8e), northern Russia, of 50% for a moving time window of 10 years are shown and the western Tibetan Plateau (Fig. 8h). The annual in Fig. 8a. Each line depicts the position of the boundary zonal-mean values of the transition latitudes and their with lighter colors representing earlier time periods. poleward retreat rates are computed over 158 longitude The changes are more noticeable over land than over intervals. Figure 8b shows northward retreat rates 2 oceans, particularly over North America and Eurasia. greater than 0.78 decade 1 over Europe within 08–308E. Figures 8c–e and 8f–h provide a zoomed view over the Also, parts of central Asia from 758 to 908E, comprising areas of significant changes. the HMA, are experiencing a significant retreat rate of 2 Over North America, 25% transition latitudes remain 0.458 decade 1. fairly stable with a little fluctuation in the Midwest and e. Changes in total snowfall and eastern United States (Fig. 8c); however, the northward snowfall-to-precipitation ratio retreat is fairly high over Europe and eastern Asia (Fig. 8f). At the 50% level, the retreat is noticeable over Focusing on the NH, the spatial trends in annual total the Canadian provinces of Manitoba, Ontario, and Quebec snowfall (snow water equivalent) from ERA-Interim and 1JANUARY 2020 T A M A N G E T A L . 51

FIG. 8. (a) Snowfall-to-rainfall transition latitudes as the boundary of potential snowfall areas with an exceedance probability of 50% over a sliding time window of 10 years, (b) the zonal-mean values of northward retreat 2 (8 decade 1, labeled pd in the figure), and the zoomed areas for different exceedance probabilities over (c)–(e) North America and (f)–(h) Eurasia. the Pentad GPCP are shown in Figs. 9a and 9b,re- snowfall trend over the southern parts of the Tibetan spectively. It is clear that compared to ERA-Interim, Plateau but they disagree over northeastern China GPCP shows more coherent declining trends over the where ERA-Interim suggests a negative trend of around 2 oceans. GPCP shows a significant declining trend of 10 mm decade 1 whereas GPCP suggests a smaller and 2 2 30 mm decade 1 over the Labrador Sea, the Baffin Bay, patchy positive trend of about 5 mm decade 1. The dis- the western coast of Greenland, and Hudson Bay in agreement between products is more pronounced over northeastern Canada. Over the Greenland Sea and the Greenland where GPCP suggests a decreasing snowfall 2 Norwegian Sea, ERA-Interim and GPCP agree that trend of around 25 mm decade 1 whereas ERA-Interim negative snowfall trends exist. Some disagreement can be reports no significant changes except over a small area observed over the northern Barents Sea where the ERA- with a coherent positive snowfall trend of around 2 Interim suggests a positive snowfall trend of around 10 mm decade 1. 2 20 mm decade 1 while GPCP shows some incoherent Figure 9c shows the trend values of annual snowfall 2 negative trend of around 30 mm decade 1. over NH climate classes and mountain ranges. Over the Over the terrestrial regions, both products agree on polar climate class, all GPCP-derived products agree on a negative total snowfall over the Midwest United States negative trend in total annual snowfall at 15.72 (15.72– 2 near Lake Superior and part of the western United 16.31) mm decade 1 whereas ERA-Interim suggests in- 2 States. Over Asia, the products agree on negative significant smaller trend value of 0.79 mm decade 1. 52 JOURNAL OF CLIMATE VOLUME 33

FIG. 9. Spatial distribution of trends in total annual snowfall (snow water equivalent) obtained from (a) ERA- Interim and (b) GPCP data over the NH, and (c) their spatial mean values over the studied Köppen–Geiger climate classes and mountain ranges. Significant trend values (a 5 0.05) are marked by an asterisk.

2 Among the three climate classes, agreement exists over around 4% decade 1. Over North America, GPCP the cold climate where they suggest comparably negative suggests that the SPR is decreasing over the Great 2 snowfall trend of around 2.77–4.48 mm decade 1.How- Plains in the United States and Manitoba, Ontario, and ever, over the arid cold climate, all GPCP combinations Quebec provinces around the Hudson Bay in Canada. suggest a positive trend in snowfall at a rate of 1.34 (0.78– Disagreement between GPCP and ERA-Interim ex- 2 2.73) mm decade 1 whereas ERA-Interim suggests a ists over the western United States, where GPCP 2 significantly negative trend of 2.77 mm decade 1.Thereis suggest a negative trend whereas a positive trend is agreement about a decreasing trend in annual snowfall suggested by ERA-Interim. In Europe, for both over the studied mountainous ranges, except over HMA. products, a significant decreasing trend is detected All GPCP-derived trends and ERA-Interim suggest over parts of Finland, Sweden, Poland, and Germany the highest decrease of annual snowfall of more than on the coastal region of the Baltic Sea as well as over 2 20 mm decade 1 over the Alps, except the combination of the United Kingdom. Central Iran, western Turkme- GPCP and NCEP–DOE R-2. Over HMA, analyses based nistan, the central Tibetan Plateau, and the Siberian on ERA-Interim suggest a significant negative trend at Plateau in Asia have been experiencing a decrease in 2 the rate of 8.42 mm decade 1, whereas the GPCP data do SPR, while an increase in parts of the Mongolian not indicate any significant trend in total snowfall. Plateau is significant and is around 4%. It should be Figures 10a and 10b show the spatial distribution of noted that in general the quality of overland satellite annual SPR trend over the NH obtained from ERA- precipitation is lower than over ocean (Kubota et al. Interim and the combination of GPCP and the en- 2009). This uncertainty could be one of the main rea- semble mean, respectively. It is evident that in GPCP sons that the detected trends are more coherent over and ERA-Interim most parts of the oceans are expe- oceans in GPCP. riencing a significant decrease in SPR; however, Over all the studied climate classes in the NH, the GPCP suggests a stronger negative trend of around trend in SPR by the ERA-Interim matches closely with 2 2 8% decade 1 compared to ERA-Interim at 4% decade 1. the one computed from the GPCP data. The largest It should be noted that in higher-latitude oceans, the decrease occurs over the polar climate region with 2 absence of a trend in GPCP is due to the unavailability 1.1% decade 1 in ERA-Interim and 1.49 (1.33–1.59)% 2 of GPCP dataset over this region. Over the terrestrial decade 1 in GPCP, followed by the cold climate region at 2 2 regions, only a few regions exhibit significant trends therateof0.68%decade 1 and 0.95 (0.75–1.02)% decade 1, 1JANUARY 2020 T A M A N G E T A L . 53

FIG. 10. Spatial distribution of trends in annual SPR over the NH, obtained from (a) ERA-Interim and (b) GPCP data and (c) their spatial mean values over the studied Köppen–Geiger climate classes and mountain ranges, as well as (d) the annual SPR values against 803 station years from the GSOD gauge station data with an SPR greater than 0.01. Significant trend values (a 5 0.05) are marked by an asterisk in (c).

respectively. However, no significant trend is observed 0.91 and 1, FAR of 0.33 and 0.34, and CSI of 0.62 and overthearidcoldclass(Fig. 10c). Among the mountain 0.66, respectively. regions, surprisingly, there is no significant trend over the western United States. There is an agreement be- 5. Conclusions and discussion tween all datasets that the highest significant decrease of SPR (2%) has occurred over the Alps, excluding In this study, we used three reanalysis datasets and the data from the NCEP–DOE R-2. All data products showed that the global-mean wet-bulb temperature denote that the HMA has experienced small but sig- trend increased significantly in the past four decades, nificantly negative trends ranging from 0.97% to except over the SH oceans. The observed regional 2 1.7% decade 1. warming trend in wet-bulb temperature is ;20% larger To validate the results of the SPR calculation, the than the regional air temperature trends of 0.0658– 2 annual values from GPCP and ERA-Interim are 0.598C decade 1 over the eastern Siberian transect ob- compared to 803 NCDC gauge station years between served during 1956–90 (Romanovsky et al. 2007) and 2 2011 and 2015 (Fig. 10d). Quality metrics including the 0.208Cdecade 1 overtheU.S.Midwest,Canadian coefficient of determination R2,percentagebias prairies, and western Arctic during 1948–2010 (Isaac (PBIAS), probability of detection (POD), false alarm and Van Wijngaarden 2012). This implies an increase in ratio (FAR), and critical success index (CSI) are used near-surface atmospheric moisture content since the (see appendix C). The results suggest that GPCP- wet-bulb temperature increases monotonically with the derived SPR values perform better than those based on relative humidity. ERA-Interim with an R2 value of 0.65 compared to 0.61 While a coherent warming trend in wet-bulb tem- and a PBIAS of 1.06% compared to 234.69%, respec- perature exists all over the Arctic region, only parts of tively. However, in terms of capturing the snowfall oc- Antarctica are experiencing a warming trend. The wet- currences, ERA-Interim and the combination of GPCP bulb temperature over Antarctica is mostly below the and the ensemble mean of the wet-bulb temperature snowfall threshold and this warming trend may not di- have comparable performance. Specifically, GPCP- rectly lead to a reduction of snowfall accumulation. derived values and ERA-Interim have POD values of However, the significant wet-bulb temperature trends 54 JOURNAL OF CLIMATE VOLUME 33

2 of ;0.48C decade 1 are lower than the air-temperature patterns of change in total snowfall and SPR. Over 2 trend of 0.568C decade 1 reported over parts of the Greenland, GPCP shows a decline in total snowfall but no Antarctica (Turner et al. 2005). This results in an in- changes in SPR while ERA-Interim shows an appreciable crease of wet-bulb depression over the years, which in increase of total snowfall and a decrease of SPR. Thus, turn increases the ablation rate at subzero temperatures from the GPCP data the total precipitation should remain (Budd 1967). constant while ERA-Interim denotes that the total pre- Among the three studied Köppen–Geiger climate cipitation has increased. classes and four mountainous regions, the NH polar class Over the Alps, not only the total snowfall but also the and the Alps are experiencing the highest warming trend. solid fraction of precipitation is decreasing significantly. On average, the Alps, the western United States, High Thus, either the total precipitation has increased or the Mountain Asia (HMA), and the Andes have experienced reduction of snowfall amount has been faster than the a reduction in potential snowfall area at 0.02 million reduction in total precipitation. Over the western United 2 km2 decade 1 with the Alps losing the highest proportion States, the total snowfall is decreasing significantly but 2 of potential snowfall areas at 3.64% decade 1.Tracking not the SPR. In other words, the decline of precipitation the transition latitudes that delineate the changes from and snowfall has been proportional. The results over snowfall-to-rainfall regimes showed an annual retreat to- HMA are ambiguous. GPCP data do not indicate any 2 ward the North Pole in the NH at 0.78 and 0.458 decade 1 significant changes in total snowfall while ERA-Interim over Europe and central Asia. denotes a significant decline. However, both datasets Data from ERA-Interim and the Global Precipitation agree that the SPR has declined. Climatology Project (GPCP) agree on a significant de- Certainly, the linkage between the changes of snow- crease of total snowfall amount over the northern At- fall and snow cover is a future line of research. Brown lantic Ocean, Greenland Sea, Norwegian Sea, and and Robinson (2011) report decreases in NH snow- 2 2 Barents Sea with a rate of 10–30 mm decade 1. Terres- cover extent of 0.8 million km2 decade 1 (7%–11%) in trial regions of total snowfall declines with a rate greater March and April over the 1970–2010 period, which is 2 than 10 mm decade 1 are over the Bitterroot Range, the consistent with the characterized changes of potential northern Rocky Mountains, the Great Plains, the U.S. snowfall areas in section 4c. Historical information on Northwest, and northern Quebec in North America; the snow-cover extent and satellite snow water equivalent United Kingdom, south of Finland, north of Germany, data (Smith and Bookhagen 2016, 2018) are needed to north of Poland, and Lithuania in Europe; and the Zagros investigate the competing effects of temperature and Mountains in the Iranian Plateau and southern Hima- precipitation trends on global changes of snow-cover layas in Asia. extent and snow water equivalent. Data from ERA-Interim and the Global Precipitation The resolution of the used reanalysis products is low Climatology Project (GPCP) agree on significant and the reanalysis and satellite precipitation estimates positive trends in annual snowfall amount of about suffer from a high degree of uncertainty. More specifi- 2 5mmdecade 1 over parts of the Tibetan Plateau, which is cally, the results reported over the mountains should be consistent with the findings by Deng et al. (2017).The interpreted with caution and should be updated when areas of agreement on SPR are over the Beaufort Sea, new higher-resolution reanalysis data with more so- the Northwest Passage, the northern Atlantic Ocean, the phisticated parameterization of the effects of topo- Greenland Sea, the Norwegian Sea, and the Barents Sea. graphic features on precipitation become available. In However, the rates in GPCP data are greater than 4% addition, reanalysis products are highly inhomogeneous while in ERA-Interim the rates are largely around 2%. since the quality, quantity, and character of assimilated Furthermore, negative trends in SPR were observed over data change over time. For example, one of the main the Great Plains and east of the Hudson Bay lowlands in reasons for the observed discrepancies between the re- North America; in Finland, Lithuania, Latvia, and Esto- analysis data over the SH is the lack of adequately dense nia in Europe; and in the Tibetan highlands in Asia, which gauge observations. This inhomogeneity can introduce are consistent with the regional studies over the United artificial trends that can affect our analyses (Long et al. States (Feng and Hu 2007; Kunkel et al. 2009), Canada 2017). Using different reanalysis products might not (Vincent et al. 2015), Finland (Irannezhad et al. 2017), completely eliminate those trend due to the assimilation and the Tibetan Plateau (Wang et al. 2016). of similar datasets. Future studies could investigate The rate of changes in SPR in GPCP seems to be snowfall changes in more homogeneous reanalyses da- systematically higher than ERA-Interim, especially over tasets such as the ECMWF’s 20th-century reanalysis oceans. Due to spatial changes in total precipitation, (Poli et al. 2016) or NOAA-CIRES’s 20th-Century there have been some differences between the global Reanalysis (Compo et al. 2011). 1JANUARY 2020 T A M A N G E T A L . 55

A similar problem exists for the analyzed Pentad where Tw is the 2-m wet-bulb temperature (K), Ta de- GPCP products because of coarse spatial resolution and notes 2-m air temperature (K), Ly is the latent heat of 21 the fact that satellite precipitation still suffers from a vaporization (J kg ), Cp refers to the specific heat 2 2 large degree of uncertainty in retrievals of orographic constant for dry air (kJ kg 1 K 1), « is the ratio of dry gas precipitation over complex terrain. Future studies can constant to water vapor gas constant, P denotes station also focus on the usage of other ancillary data such as pressure (hPa), RH is the relative humidity, and A 5 vertical temperature lapse rate for characterizing pre- 2.53 3 109 hPa and B 5 5420 K are empirical constants. cipitation phase to improve the inference over mountain Due to the lack of information on RH within ERA- ranges. Moreover, finding ways to refine our inference Interim, it was computed from dewpoint temperature using snowfall data from recent spaceborne active ra- and air temperature using Eq. (A2) provided by ECMWF dars on board the GPM and CloudSat satellites could (2015): be another future line of research. T 2 273:16 T 2 273:16 And last, it is important to note that the uncertainty of 5 : d 2 a RH exp 17 502 2 : 2 : , our analysis and the derived conclusions are subject to Td 32 19 Ta 32 19 the accuracy of the data used and techniques explained (A2) such as the lower skill of precipitation phase-partitioning methods at near-freezing temperature (Ding et al. 2014; where Td is the dewpoint temperature (K). Jennings et al. 2018). In particular, we did not make any correction for the effects of topography on both tem- perature and precipitation data and only extracted the APPENDIX B information content of the available observational data- sets. Developing globally accepted relationships for such Details of Statistical Trend Analysis corrections over important mountainous regions of the world would help to advance climate change assessments For brevity, here we explain the Theil–Sen method for in regions with complex topography. trend analysis adopting the notation only for the wet- bulb temperature. To that end, let us assume that 5 1 2 ... n Acknowledgments. The first and second authors Twb fTwb, Twb, , Twbg represents annual time se- acknowledge support from the National Aeronau- ries of hemispheric-mean wet-bulb temperatures for 1 2 n tics and Space Administration (NASA) Precipita- year y 5 fy , y , ..., y g. The Theil–Sen estimate of the tion Measurement Project (NNX16AO56G), New linear slope b is defined as (Early Career) Investigator Program award (NIP; ! j 80NSSC18K0742), and the grant from the Terrestrial T 2 Ti b 5 median wb wb , i 5 1, 2, ..., n 2 1, Hydrology Program (THP; 80NSSC18K152). The first yj 2 yi author also acknowledges the support provided by j 5 2, 3, ..., n, j . i. (B1) Sommerfield Graduate Fellowship at University of Minnesota–Twin Cities during his first year of study. Numerous tests have been examined to quantify the NCAR is sponsored by the National Science statistical significance of the Theil–Sen estimator, here we Foundation. adopt the bootstrap Mann–Kendall (MK) test. In sum- mary, the MK test computes the following test statistic:

n21 n APPENDIX A 5 å å j 2 k S sgn(Twb Twb), (B2) k51 j5k11 Computation of the Wet-Bulb Temperature where j . k and sgn() refers to the signum function. Pos- Here, the wet-bulb temperature is calculated from itive (negative) values of S imply a positive (negative) trend Eq. (A1) (Stull 2016) using an iterative Newton–Raphson in the time series. Under the null hypothesis, Kendall (1948) method: showed that the test statistic S is asymptotically a zero-mean normally distributed random variable with variance 2 3 ​q Var(S) 5 n(n 2 1)(2n 1 5) 2 å t (t 2 1)(2t 1 5) /18, L 1 RH i51 i i i T 5 T 2 y E ​A4 2 5, where, q is the total number of groups of same observa- w a C B B p P exp 2 A P exp 2 A tions or ties and t is the number of observation in the ith T T i w a tied group. Thus, the standard test statistic Z is defined as (A1) follows: 56 JOURNAL OF CLIMATE VOLUME 33

TABLE C1. Statistical measures for performance evaluation of the derived wet-bulb temperature and SPR.

Index Formula Range 2 ( ) Coefficient of determination (R ) 2 0to1 Ns ^ 2 m 2 m 1 å xML(i) ML xG(i) G 2 s s Ns 1i51 ML G

2‘ 1‘ Percent bias (PBIAS) Ns to å [x^ML(i) 2 xG(i)] 5 i 1 3 100 Ns å xG(i) i51

Probability of detection (POD) nH 0to1 nH 1 nM

False alarm ratio (FAR) nF 0to1 nH 1 nF

Critical success index (CSI) nH 0to1 nH 1 nM 1 nF

8 > S 2 1 If the MK test statistic S of the original time series is > pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi if S . 0 > V higher than the 97.5th percentile or lower than 2.5th <> ar(S) percentile of the empirical distribution of test statistic S*, 5 5 Z > 0ifS 0 , (B3) the hypothesis, that there is no trend in the data, is re- > > 1 > pSffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 , jected. Throughout, for computation of the empirical : if S 0 5 Var(S) distribution of MK test statistic, we set B 3000.

$ where the null hypothesis can be rejected if jZj Z12a/2, APPENDIX C at level of significance a. The asymptotic null distribution of the MK test sta- Quality Metrics tistic S;~ N [0, Var(S)] is valid under the assumption of serial independence (von Storch 1995). To formally ac- Table C1 shows the used quality metrics in this study: x^ (i) is the maximum likelihood estimate for ith station count for the effects of serial dependence, we confine ML day (or year) with standard deviation s , x (i) is the our consideration to the classic moving-block bootstrap ML G corresponding gauge observation with standard de- (MBB; Liu and Singh 1992). viation s , N is the total number of station days (or Specifically, let us assume that S is the MK G s years), and m and m are the mean of ML estimates test statistic of the original annual time series ML G 1 2 n and gauge observations, respectively. In computation of Twb 5 fT , T , ..., T g. Given the time series, a wb wb wb n serial correlation length r at significance level a is the false alarm ratio and critical success index, H is the n n computed and the length of the block is set to l 5 r 1 1. number of hits, M is the number of misses, and F is the number of false alarms. The probability of detection The time series Twb is then divided into N 5 n 2 l 1 1 1 2 (POD) value refers to the proportion of correctly overlapping blocks j : 5 fTi , ..., Ti l 1g, with proba- i wb wb identified number of snowfall occurrences, the false bility of occurrence equal to 1/N, where i 5 1, ..., N and alarm rate (FAR) refers to the proportion of incorrectly l/n / 0asn, l / ‘. A number of k 5 n/l blocks b b b identified number of snowfall occurrences, and the fj* , j* , ..., j* g are sampled with replacement from 1 2 k critical success index (CSI) penalizes both misses and j1, j2, ... , jN and concatenated to reconstruct B boot- b b b false alarms. strap pseudo time series as T*b 5 fj* , j* , ..., j* g, wb 1 2 k where b 5 1, 2, ..., B. Bootstrap empirical distribution of MK test statistic S* is obtained from the pseudo REFERENCES bootstrap time series T*b and the significance of trend is wb Adler, R. F., and Coauthors, 2003: The version-2 Global Precipitation finally computed by applying a two-tailed hypothesis test. Climatology Project (GPCP) monthly precipitation analysis 1JANUARY 2020 T A M A N G E T A L . 57

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