Spatial Representativeness Analysis for Snow Depth Measurements of Meteorological Stations in Northeast China

APRIL 2020 W A N G A N D Z H E N G 791

YUANYUAN WANG AND ZHAOJUN ZHENG National Satellite Meteorological Center, China Meteorological Administration, Beijing, China

(Manuscript received 14 June 2019, in ﬁnal form 20 February 2020)

ABSTRACT

Triple collocation (TC) is a popular technique for determining the data quality of three products that estimate the same geophysical variable using mutually independent methods. When TC is applied to a triplet of one point-scale in situ and two coarse-scale datasets that have the similar spatial resolution, the TC-derived performance metric for the point-scale dataset can be used to assess its spatial representativeness. In this study, the spatial representativeness of in situ snow depth measurements from the meteorological stations in northeast China was assessed using an unbiased correlation metric r2 estimated with TC. Stations are t,X1 considered representative if r2 $ 0:5; that is, in situ measurements explain no less than 50% of the variations t,X1 in the ‘‘ground truth’’ of the snow depth averaged at the coarse scale (0.258). The results conﬁrmed that TC can be used to reliably exploit existing sparse snow depth networks. The main ﬁndings are as follows. 1) Among all the 98 stations in the study region, 86 stations have valid r2 values, of which 57 stations are t,X1 representative for the entire snow season (October–December, January–April). 2) Seasonal variations in r2 t,X1 are large: 63 stations are representative during the snow accumulation period (December–February), whereas only 25 stations are representative during the snow ablation period (October–November, March–April). 3) The r2 is positively correlated with mean snow depth, which largely determines the global decreasing t,X1 trend in r2 from north to south. After removing this trend, residuals in r2 can be explained by hetero- t,X1 t,X1 geneity features concerning elevation and conditional probability of snow presence near the stations.

1. Introduction Validation of microwave snow depth products with ground truth data is key to improving inversion al- Snow cover is a key component in the global water gorithms. However, owing to the high spatial vari- cycle and directly impacts the Earth’s energy balance ability of snow depth, the validation process can be and climate dynamics (Cohen 1994). Remote sensing is quite challenging. An in situ snow depth measurement the most efficient way to regularly measure snow cover can only be representative over a very small spatial and depth on global and regional scales (Armstrong scale (Clark et al. 2011; Trujillo et al. 2007), whereas and Brodzik 2002; Foster et al. 2011). The Scanning satellite-derived snow depth represents the mean Multichannel Microwave Radiometer (SMMR), Special value of a microwave footprint with a size of 25 km 3 Sensor Microwave Imager (SSM/I), and Advanced 25 km or larger (Vander Jagt et al. 2013). If satellite- Microwave Scanning Radiometer for Earth Observing derived snow depth is directly compared with point System (AMSR-E) have been routinely used to retrieve measurements, the obtained errors are likely domi- snow depth and snow water equivalent (SWE) since nated by representativeness errors due to the vari- the 1970s (Che et al. 2016). Satellite snow products are ability of the snow depth field on subgrid scales as increasingly used for modeling and monitoring in vari- opposed to snow depth inversion model errors ous fields such as hydrology (Berezowski et al. 2015), (Brasnett 1999; Tustison et al. 2001; Chang et al. 2005; climate research (Bormann et al. 2012), glaciology Liston 1999, 2004). (Stroeve et al. 2005), and numerical weather prediction To evaluate the spatial representativeness of the (Brasnett 1999). point-scale snow depth, most studies attempted to obtain the difference between the point measurement Corresponding author: Yuanyuan Wang, wangyuany@ and the area average, and argued that a point mea- cma.gov.cn surement is representative if its value deviates less than

DOI: 10.1175/JHM-D-19-0134.1 Ó 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 792 JOURNAL OF HYDROMETEOROLOGY VOLUME 21

10% from the area average (Neumann et al. 2006; questions, which have not been fully explored in previ- Molotch and Bales 2005, 2006; Rice and Bales 2010; ous TC studies. Meromy et al. 2013; Grünewald and Lehning 2013; 1) How representativeness varies with season? Grünewald et al. 2013). This method requires a dense Representativeness of a station is not a constant sampling network, based on which upscaling to the (Bohnenstengel et al. 2011); it can change con- coarse scale can be achieved by using spatial modeling siderably from the snow accumulation period to methods. Although this method has been success- the snow ablation period owing to the varia- fully applied at the watershed scale, it is of limited tions in the spatial heterogeneity of snow depth use for estimating the spatial representativeness of (Molotch and Bales 2005; Winstral and Marks sparse meteorological stations that provide only one 2014). Some researchers argued that the obser- in situ observation for a satellite footprint. Since it vations need to be selected with the specific is logistically prohibitive to carry out extensive snow objective of representing either the accumulation surveys or set up dense networks over hundreds of op- or the ablation season process (Molotch and erational meteorological stations, the limitations of Bales 2005). Understanding the seasonal varia- point measurements at these stations in adequately tions in representativeness can help us choose the representing snow depth for the surrounding area have most representative stations according to the been questioned but not explored in detail (Blöschl time of the snow depth product and hence make 1999; Neumann et al. 2006; Derksen et al. 2003; Chang full use of the existing networks. et al. 2005; Grünewald and Lehning 2013; Meromy 2) What factors in the vicinity of stations play a et al. 2013). dominant role in determining representativeness? A promising way to evaluate the representativeness Understanding the dominant factors has two advan- of a point-scale dataset is the triple collocation (TC) tages. First, it provides an indirect approach to validate technique, which estimates the data quality of three representativeness assessments. Strong heterogeneity mutually independent datasets without treating any usually results in low representativeness; thus, the dataset as perfectly observed ‘‘truth’’ (Stoffelen 1998). representativeness assessments are generally reason- TC has now become a standard procedure in compre- able if they are strongly correlated with hetero- hensive satellite validation processes, especially in soil geneity features. Second, dominant factors can be moisture research (Scipal et al. 2008; Dorigo et al. 2010, used to predict representativeness, which is poten- 2015; Chen et al. 2017; Gruber et al. 2016a,b, 2017). tially useful in choosing the representative locations When TC is applied to a triplet containing one point- for new sites. scale and two coarse-scale datasets that have the similar spatial resolution, performance metrics associated with The remainder of this paper is organized as follows. the point-scale dataset indicate its spatial representa- Section 2 introduces the TC technique and how TC is tiveness, assuming that the instrumental random error used to evaluate station representativeness. Section 3 can be neglected (Gruber et al. 2013, 2016a; Chen et al. describes the study region, datasets, TC implementation 2017). The most prominent feature of using TC to assess process, and the method of extracting heterogeneity fea- the spatial representativeness is that it is data-driven and tures. Results and discussion are presented in sections 4 does not need field surveys or dense sampling net- and 5, respectively. works. The credibility of using the TC-derived correlation metric or random error variances in representing 2. Introduction of the TC technique the closeness of the point-scale data to the coarse-scale ground truth has been confirmed at densely in- a. TC approaches strumented validation sites by Miralles et al. (2010) The most commonly used error model for TC analysis and Chen et al. (2017). is the following model (Gruber et al. 2016a): Validations of microwave snow depth and soil moisture share a high degree of similarity. The success of 5 a 1 b 1 « Xi i it i , (1) TC applications in soil moisture studies has prompted us to adopt this technique for snow depth studies. where Xi (i 2 {1, 2, 3}) are three collocated and inde- To the best of our knowledge, this study is the first at- pendent datasets of the same geophysical variable line- tempt to apply TC to evaluate the spatial representa- arly related to the true underlying value t with additive tiveness of point-scale snow depth measurements from zero-mean random errors «i.ThetermsXi, t, «i are meteorological stations. Besides assessing the spatial all random variables; ai and bi are the intercepts and representativeness, we investigated the answers to two slopes, respectively, representing systematic additive

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC APRIL 2020 W A N G A N D Z H E N G 793 8 and multiplicative biases of dataset Xi with respect to 2 Q12Q13 > s« 5 Q 2 the true signal t. > 1 11 Q > 23 There are four main underlying assumptions for the > <> error model of TC (Zwieback et al. 2012; Gruber 2 Q12Q23 s« 5 Q 2 . (6) > 2 22 et al. 2016a,b): (i) linearity between the true signal > Q13 > and the observations; (ii) signal and error stationarity; > > (iii) error orthogonality: independence between the : 2 Q13Q23 s« 5 Q 2 « 5 3 33 errors and the true signal, that is, Cov(t, i) 0; and Q12 (iv) zero error cross correlation: independence be- 2 « « 5 Since s« is the absolute random error variance af- tween the errors of Xi and Xj,thatis,Cov( i, j) 0, i for i 6¼ j. fected by the dynamic range of the data, Draper et al. Following McColl et al. (2014), the covariances be- (2013) proposed relative error variance (fMSEi), which tween the different datasets are calculated as follows: is calculated by normalizing the error variances with the corresponding dataset variances: 5 2 Cov(Xi, Xj) E(XiXj) E(Xi)E(Xj) 2 s« 5 b b s2 1 b « 1 b « fMSE 5 i . (7) t Cov(t, ) Cov(t, ) i i j i j j i Qii 1 « « Cov( i, j), (2) Combining (7), (4), and (3), fMSEi can be written as s2 5 follows: where t var(t). Using the assumptions of error orthogonality and zero error cross correlation, the equa- 2 2 s« s« tion is reduced to (3): fMSE 5 i 5 i , (8) i u2 1 s2 b2s2 1 s2 i « i t « ( i i b b s2 6¼ i j t , for i j [ 5 2 2 2 Q Cov(X , X ) , (3) where b s represents the signal and s« represents the ij i j 2 2 i t i b b s 1 s« , for i 5 j i j t i noise (Gruber et al. 2016a; McColl et al. 2014); thus, fMSE is not only a measure of relative error, but also a 2 i where s« 5 var(«i), representing the variance of i measure of signal-to-noise ratio (SNR). Furthermore, random error in dataset Xi. Since there are six fMSEi is related to the linear correlation coefficient of equations (Q11, Q12, Q13, Q22, Q23, Q33) but seven r Xi with the underlying true signal t (denoted by t,Xi). unknowns (b , b , b , s« , s« , s« , s ), the system is 1 2 3 1 2 3 t According to McColl et al. (2014), the relationship be- underdetermined. It can be solved by defining a new tween r and the ordinary least squares (OLS) slope b u 5 b s t,Xi i variable i i t. Then, the equations can be re- can be written as in (9): written as in (4): ( b s u u , for i 6¼ j r 5 piffiffiffiffiffiffiffit i j t,X . (9) Q 5 . (4) i Q ij 2 2 ii u 1 s« , for i 5 j i i Combining (7), (8), and (9), we obtain (10): Now there are six equations and six unknowns, and u2 2 2 the system can be solved. Variable i , which provides b2s2 Q 2 s« s« r2 5 i t 5 ii i 5 2 i 5 2 estimates of the sensitivity of datasets X to ground truth t,X 1 1 fMSE . (10) i i Q Q Q i changes (Gruber et al. 2016a), can be written as follows: ii ii ii 8 r2 Q Q Equation (10) indicates that t,X and fMSEi are > u2 5 b2s2 5 12 13 i > 1 1 t Q complementary. When fMSEi is 0.5, the coefficient of > 23 r2 > determination t,X for the linear error modelpffiffiffiffiffiffiffi is 0.5, and <> i Q Q the correlation coefficient of Xi with t is 0:5 (’0.71). u2 5 b2s2 5 12 23 > 2 2 t . (5) > Q13 b. Representativeness analysis of point-scale data > > with TC > Q Q : u2 5 b2s2 5 13 23 3 3 t While TC is a powerful tool for estimating random Q12 errors and removing systematic differences between the The estimation equation for error variances can be signal variance component of observations, it is affected written as follows: by representativeness errors (Yilmaz and Crow 2014).

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 794 JOURNAL OF HYDROMETEOROLOGY VOLUME 21

TC assumes that the three datasets represent the same regions in China (Li et al. 2008) and is characterized by signal, which is very unlikely given that the three datasets taiga snow (Sturm et al. 1995). The region with a total can have very different spatial measurement support area of 1.26 3 106 km2 encompasses the provinces of (McColl et al. 2014; Gruber et al. 2016a). When a triplet Heilongjiang, Jilin, Liaoning, and the eastern part of consists of one point-scale in situ dataset and two coarse- Inner Mongolia. The regional climate includes warm scale datasets that have the similar spatial resolution, the temperate, medium temperate, and subarctic zones. high-resolution signal in the point-scale dataset cannot be Annual precipitation is approximately 430–680 mm, of detectable for coarse-scale datasets and therefore be re- which 5%–10% is snowfall (He et al. 2013; Zhang et al. garded as error (Gruber et al. 2016a). In other words, TC 2016). There are three mountain ranges (Daxinganling, will penalize the point-scale dataset for its limited rep- Xiaoxinganling, and Changbaishan Mountains) and two resentativeness at the coarse scale, whereas no repre- large plains (Songnen and Sanjiang) in the region. sentativeness error is assigned to the error estimates of Primary land cover types are forest (40%), farmland the coarse-scale datasets (Gruber et al. 2016a; Yilmaz and (30%), and grassland (20%). Figure 1 shows the spatial Crow 2014). This characteristic of TC opens an oppor- pattern of tree cover (%) and elevation (m) in the tunity for evaluating the spatial representativeness of study region. point-scale data efficiently, which has been proved feasi- b. Data ble by recent studies on soil moisture validation networks (Gruber et al. 2013; Chen et al. 2017; Miralles et al. 2010). 1) METEOROLOGICAL Although most previous works used random error variances s2 to evaluate representativeness (Gruber There are 98 operational meteorological stations lo- «i et al. 2013), which is an absolute error metric and sen- cated within the study region. Figure 1 shows that in sitive to data range and variability, more recent studies general, these stations are evenly distributed, although recommend using the correlation metric r2 (Chen et al. more stations are located on plains than in mountains. t,Xi 2017; Gruber et al. 2017). As a unitless measure, r2 can Snow depth and snow density are measured manually t,Xi be fairly compared across space and time. Moreover, r2 using a snow tube with a cross-sectional area of 100 cm2 t,Xi is interpretable, making it easier to choose a threshold at the fixed snow experiment field at each station. value. In this study, we assume that the value of r2 for a Measurement frequency is one every day for snow depth t,Xi representative station should be equal to or larger than and every five days for snow density, and each record 0.5. This criterion has been used in other studies (Chen et is obtained from the average of three measurements a1. 2017) and can be interpreted as follows: a station is (Dai and Che 2011). representative if its measurements can explain no less 2) SATELLITE SNOW DEPTH FROM GLOBSNOW than 50% of the variance in the ground truth of the area PRODUCT average, or from the SNR perspective, the signal level contained in the in situ measurements is no less than the The daily GlobSnow snow water equivalent (SWE) r noise level. Since t,Xi represents the correlation between product (version 2.0) from 2000 to 2013 was down- Xi and t, the criterion can also be interpreted as follows: a loaded at http://www.globsnow.info/. The product was station is representative if the correlation coefficient be- retrieved by using a data-assimilation-based approach tween in situ measurements and the groundpffiffiffiffiffiffiffi truth of the which combines spaceborne passive radiometer data area average is equal to or larger than 0:5 (’0.71). (SMMR, SSM/I, and SSMIS) with data from ground- Note that TC assumes stationarity of random error based synoptic weather stations (Pulliainen 2006; variance, thus, the representativeness estimates represent Takala et al. 2011). According to Takala et al. (2011), 2 the averaged condition of the entire period (Loew and constant snow density (0.24 g cm 3)canbeusedto Schlenz 2011). Considering that error is often time vari- convert SWE to snow depth. GlobSnow SWE infor- ant, the result for the entire period can be inaccurate for a mation is provided for terrestrial nonmountainous particular subset of the time period. If representativeness regions of the Northern Hemisphere, excluding gla- of a particular time period is of interest, data inputs ciers and Greenland. The product has been validated should be confined within the corresponding time period. using independent SWE reference data from Russia, the former Soviet Union, Finland, and Canada, and 3. Study region, data, and methods the results indicate overall strong retrieval performance with root-mean-squared error (RMSE) below a. Study region 40 mm for cases when SWE is below 150 mm. Retrieval The study region is northeast China (388–568N, 1208– uncertainty increases when SWE is above this threshold 1358E), which is one of the three primary snow-covered (Takala et al. 2011). The GlobSnow results over China

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC APRIL 2020 W A N G A N D Z H E N G 795

FIG. 1. Tree cover (provided by MOD44B), elevation (provided by GTOPO30), and distribution of meteorological stations in the study region. are based on passive microwave information because no optical snow cover results, the CMC snow depth data Chinese stations are available for data assimilation, show more skill than climatology (Brasnett 1999). Since which ensures the independence between the GlobSnow snow depth observations in China are not available in data and meteorological observations in this study. the CMC snow depth analysis system, the snow depth results for China are model derived, which are the initial 3) SNOW DEPTH ANALYSIS DATA FROM CMC guess field of the simplified assumptions regarding Canadian Meteorological Centre (CMC) daily snow snowfall, melting, and aging. depth analysis data (version 1) from 2000 to 2013 4) SATELLITE SNOW COVER were downloaded at https://nsidc.org/data/NSIDC-0447 (Brown and Brasnett 2010). The snow depth production Representativeness of in situ snow depth measure- includes two steps (Brasnett 1999). The first step is to ments is largely determined by the spatial heterogeneity calculate the background field of snow depth based on of snow depth in the surrounding area. Due to the un- the forecasts of precipitation and the analysis of screen- availability of subgrid scale snow depth distribution level temperature. Specifically, precipitation is consid- near a station, optical satellite snow cover data with a ered snow if the analyzed screen-level temperature is high spatial resolution are often used as a substitute zero or less. The snow melting algorithm is applied when (Molotch and Bales 2005, 2006). In this study, the ‘‘binary’’ the analyzed temperature is greater than zero. When (i.e., snow or not snow) snow cover map provided by the there is neither snowfall nor melting, it is assumed that MODIS daily snow cover product (MOD10A1, from the mass of the snowpack is conserved. The next step is 2000 to 2013) with a spatial resolution of 500 m was used. to incorporate the snow depth observations wherever The MODIS snow mapping algorithm is based on a they are available by performing statistical interpolation normalized difference snow index (NDSI) approach. every 6 h on a 1/38 grid. Compared to the microwave and Normalized difference vegetation index (NDVI) criteria

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 796 JOURNAL OF HYDROMETEOROLOGY VOLUME 21 are also applied to enable snow detection in areas with Previous research demonstrated that raw values dense vegetation (Dong and Menzel 2016). Many stud- with varying dynamic ranges and climatology tend ies have confirmed high accuracy and consistency of to violate TC assumptions (Gruber et al. 2016a; MODIS snow cover images by comparing them with Dorigo et al. 2010; Chen et al. 2017). Therefore, we other high spatial resolution satellite-derived snow prod- calculated the snow depth anomaly by removing ucts or ground-based point snow depth measurements climatological signals from the raw time series of (Maurer et al. 2003; Hall and Riggs 2007). each product. The climatology was obtained by first averaging multiannual data for each day of year 5) OTHER ANCILLARY DATA (DOY) and then smoothed by a moving window Forest coverage is a potentially important factor that of 7 days. influences station representativeness and satellite snow Using the triplet data consisting of in situ observed depth product quality (Vander Jagt et al. 2013). Snow snow depth anomaly (represented by X1), satellite- depth tends to be underestimated because forest atten- estimated snow depth anomaly (GlobSnow product uation and its upwelling radiation can decrease the represented by X2), and snowpack model-estimated passive microwave brightness temperature signal from snow depth anomaly (CMC product represented by snow cover underneath (Chang 1996). Meanwhile, op- X3), we calculated the correlation coefficients between erational meteorological stations measure snow depth in any two of the three anomaly time series for each sta- clearings where snow dynamics differ from those in the tion. Those stations that failed to show significant posi- forest (Raleigh et al. 2013). Therefore, stations located tive correlation (p value . 0.05) or had less than 100 near dense forests tend to have problems representing data points in the collocated triple time series were the surrounding environment. In this study, the MODIS considered unqualified and masked from the TC anal- percent tree cover product (MOD44B, with a spatial ysis. To analyze the seasonal variation in representa- resolution of 500 m) was used to extract the mean tiveness, we divided the collocated time series into two forest coverage for the surrounding area of each sta- periods: 1) stable or accumulation period (December– tion (Hansen et al. 2002). February) when temperature is very low and snow often Elevation is another important factor that needs to be accumulates steadily and 2) unstable or ablation period considered (Jost et al. 2007; Grünewald et al. 2013). (October, November, March, April) when temperature Complex topography within a microwave footprint is higher and fast snowmelt may result in patchy and makes it difficult to extract the snow signature. Different heterogeneous snow distribution. For each period, un- viewing angles of mountains by the ascending and de- qualified stations (no significant positive intercorrela- scending orbits further complicate the problem (Chang tion or sample size is less than 100) were excluded from and Rango 2000). Grids with high standard deviations of the TC analysis. elevation are often excluded from interpolation or as- 2) EXTRACTION OF EXPLANATORY VARIABLES similation analysis (Takala et al. 2011). In this study, the global DEM data (GTOPO30, with a spatial resolution of All explanatory variables were extracted from a win- approximately 1 km) were used to extract standard devi- dow region centered around each station. The window ations of elevation in the surrounding area of each station. region has a spatial extent of 51 pixels 3 51 pixels (a c. Methods pixel is 500 m), approximately the same size of a microwave grid. Mean forest coverage data (MFC) were extracted from the MOD44B product. The terrain index 1) TC ANALYSIS (TI), which is defined as the standard deviation of ele- Daily snow depth measurements at each meteoro- vation within the window region, was extracted from logical station in the snow season (October–December, the GTOPO30 product. With regard to the snow cover January–April) from 2000 to 2013 were used. The data climatology features, eight variables were designed were passed through temporal consistency and range and extracted from the MOD10A1 ‘‘binary’’ data checks. Each record has a quality control flag and only over 2000–13. high-quality data were used in the analysis. According to Regional mean and standard deviation of snow cover the longitude and latitude of a station, we located the frequency in the surrounding area of a station is calcu- microwave grid (25 km 3 25 km) whose center is the lated as follows: closest to the station and extracted the snow depth value 8 from both GlobSnow and CMC products. Samples with < mFsnow 5 mean(Fsnow ) i,j , (11) all three collocated data exhibiting zero values were : vFsnow 5 std(Fsnow ) removed from the analysis. i,j

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC APRIL 2020 W A N G A N D Z H E N G 797 where Fsnowi,j is the accumulated snow cover frequency Using the similar formula, regional mean and stan- for pixel (i, j) in the window region over time span T (i.e., dard deviation of conditional probability of nonsnow 14 snow seasons over 2000–13). presence are calculated as follows: 8 T < 5 å mPland mean(Plandi,j) snowi,j,n , (17) n51 : 5 Fsnow 5 , (12) vPland std(Plandi,j) i,j T 5 where snowi,j,n 1, if pixel (i, j) is covered by snow at where Plandi,j is the probability of nonsnow presence at time n; otherwise, snowi,j,n 5 0. pixel (i, j) when the station (center pixel) is not covered The presence of snow-free land in the cold season by snow: means no snow or snow has melted, which provides T T somewhat different information from snow cover 5 å å Plandi,j Li,j,n= Lcenter,n, (18) frequency. Using the similar approach, regional mean n51 n51 and standard deviation of nonsnow cover frequency åT in the surrounding area of a station is calculated as where n51Lcenter,n is the number of days the station is åT follows: not covered by snow; n51Li,j,n is the number of days 8 neither the pixel (i, j) nor the station is covered by snow. < mFland 5 mean(Fland ) Note that the snow climatology features were extracted i,j , (13) from the cloud-free data; thus, they are biased to the : vFland 5 std(Fland ) i,j clear-sky condition. Considering that snow depth has a time-integrative nature and will not change quickly with where Flandi,j is the accumulated non–snow cover fre- sky conditions, we assume that such a bias will not have a quency for pixel (i, j) in a window region over time signiﬁcant impact on climatological results. span T:

T 4. Results å landi,j,n 5 a. Representativeness assessments for the entire Fland 5 n 1 , (14) i,j T period Among 86 stations that can output valid TC results for where landi,j,n 5 1, if pixel (i, j) is not covered by snow at 5 the entire period, 57 stations have r2 values larger than time n; otherwise landi,j,n 0. t,X1 If a station is representative, then when it is covered 0.50, indicating that 66% of the stations are spatially by snow, its surrounding area should also be covered representative. Among the remaining 29 stations, 26 have moderate representativeness (0:25 # r2 , 0:5), by snow with high probability. This consistency infor- t,X1 and 3 have low representativeness (0 , r2 , 0:25). mation cannot be extracted from mFsnow or vFsnow. t,X1 Therefore, we calculated the regional mean and stan- Table 1 shows that the average value and standard deviation of r2 are 0.59 and 0.19, respectively. The spatial dard deviation of conditional probability of snow pres- t,X1 distribution of r2 is shown in Fig. 2a. Stations with low ence as follows: t,X1 or no representativeness are generally located in the 8 southern region, whereas the representative stations are < mPsnow 5 mean(Psnow ) i,j in the northern region. Stations with moderate repre- : 5 , (15) vPsnow std(Psnowi,j) sentativeness are mainly located in the southern region, but some of them are mixed with representative stations where Psnowi,j is the probability of snow presence at near the northern mountainous region. pixel (i, j) when the station (center pixel) is covered by b. Seasonal variations in representativeness snow (Dong and Menzel 2016): Statistical parameters of r2 are shown in Table 1, t,X1 T T where r2 for the unstable period is noticeably lower Psnow 5 å S = å S , (16) t,X1 i,j i,j,n center,n than r2 for the stable period. If the same threshold n51 n51 t,X1 r2 $ : ( t,X 0 5) is used, the number of representative sta- T 1 where ån51Scenter,n is the number of days the station is tions for stable and unstable periods is 63 and 25, re- T snow covered; ån51Si,j,n is the number of days both pixel spectively. Therefore, more stations can be used for (i, j) and the station are snow covered. coarse-scale data validation during the stable period

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 798 JOURNAL OF HYDROMETEOROLOGY VOLUME 21

r2 2 TABLE 1. Statistics of t X for different periods. The number in Table 2 also shows the correlation coefficients of r , 1 t,X1 the parentheses represents the number of stations with valid TC with explanatory variables for both stable and unstable results. periods. Only mFsnow, mFland, and mean_SD are r2 Median Mean Std dev highly correlated with r2 , regardless of the season t,X1 t,X1 Entire period (86) 0.63 0.59 0.19 analyzed. The correlation during the unstable period is Stable period (90) 0.67 0.64 0.21 noticeably stronger. Since mFsnow and mFland are Unstable period (62) 0.44 0.45 0.22 strongly correlated with mean_SD, we infer that stations with deeper snow tend to have better representativeness. Since snow depth in the northern region is larger, (Fig. 2b). By contrast, only a small number of stations the northern stations are generally more representative can be reliably used during the unstable period, and than the southern stations, and this is partly attributed to these stations are mainly located in the northern cold the definition of r2 . Being a relative error metric, r2 t,X1 t,X1 region or in the middle region with flat terrain (Fig. 2c). tends to favor data with larger variations, which is the Owing to a lower sampling density and weaker posi- case for northern stations with deeper snow. tive correlations among the three snow depth products, Besides the smooth latitudinal trend in r2 , local t,X1 the number of stations that can output valid represen- variations in representativeness are also evident (Fig. 2). tativeness results for the unstable period is only 62, while It is important to identify the factors that affect local it is 90 for the stable period. For a fair comparison, the variations because the task of choosing a representative following analysis is based on 61 stations that output location for a new site is often spatially confined within a valid results for both periods. The scatterplot of r2 region where climatic variations can be neglected. We t,X1 (Fig. 3a) shows that most points are under the 1:1 line, tried all possible combinations of two variables (except indicating that stations are generally less representative mean_SD) to model the residuals in r2 that cannot t,X1 during the unstable period. Some points deviate from be explained by mean_SD. The model incorporating the 1:1 line dramatically, suggesting that they suffer mPsnow and TI as independent variables showed the large reductions in representativeness when the period highest accuracy. The linear regression model with three shifts. Twenty-nine stations that are representative during variables (mPsnow, TI, mean_SD) achieved satisfactory the stable period become nonrepresentative during the performance (r 5 0.70) in estimating r2 for the unstable t,X1 unstable period. However, there are four stations show- period, but the model accuracy was less satisfactory (r 5 ing slightly higher representativeness values during the 0.54) for the stable period due to the weaker correlations r2 unstable period. With regard to the standard deviation of between t,X and explanatory variables. s 1 random errors «1, a less pronounced seasonal variation is observed (Fig. 3b). Most points are scattered around the s 1:1 line. Several stations show higher values of «1 during 5. Discussion the stable period, most likely due to a larger magnitude of a. Definition of representativeness snow depth. Previous studies have argued that a point measure- c. Explaining representativeness ment is representative if its value deviates less than 10% Prior to the representativeness modeling, we analyzed from an area average. This requirement may be appli- the correlation coefficients among the explanatory var- cable when choosing representative locations for new iables (Table 2). There are several pairs of variables sites, but for existing networks, it is too stringent. showing very strong correlations, such as mPsnow and Finding stations that fulfill such a requirement can be vPsnow, mFland and mean_SD, mFsnow and mFland, very difficult or even impossible (Molotch and Bales vPsnow and TI, and vFsnow and MFC. Specifically, two 2005). Due to the stable physiographic features and variables related to the conditional probability of snow similar meteorological forcing conditions from year to presence (mPsnow, vPsnow) are strongly related to year, a station’s measurements can be consistently lower two physiographic factors (TI and MFC). Three var- or higher than the area average of its surroundings iables related to the mean frequency of snow or land (Liston 2004; Deems et al. 2008; Schirmer et al. 2011; Nitta occurrence (mFsnow, vFsnow, mFland) are strongly et al. 2014), suggesting that a large fraction of the differ- correlated with the mean snow depth of the stations ence has a systematic nature. If this systematic difference (mean_SD). The results indicate that information can be corrected and the in situ measurements match overlap exists between snow climatology features and the area average value after the correction, then the sta- physiographic characteristics in the surrounding area tion should be considered representative. Therefore, we of the stations. prefer the definition in Vanderlinden et al. (2012) that

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC APRIL 2020 W A N G A N D Z H E N G 799

FIG. 2. Spatial distribution of r2 for the (a) entire t,X1 period, (b) stable period, and (c) unstable period.

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 800 JOURNAL OF HYDROMETEOROLOGY VOLUME 21

2 FIG. 3. Comparison for (a) representativeness measure r and (b) random error standard deviations s« between stable and t,X1 1 unstable period.

representative locations are the locations where mea- majority (signal shared by X2 and X3) and punishes 2 surements are either close to the average values or can minority (signal only from X ). Therefore, s« and r 1 i t,X1 be easily transformed to obtain the average values. can be used to assess the spatial representativeness of s The largest obstacle to evaluating representativeness the point-scale dataset. Note that «i is not the root- is the lack of area averages (i.e., ground truth at the mean-square difference (RMSD) between X1 and t, but footprint scale) against which a station can be compared the RMSD between linear-corrected (or upscaled) X1 and corrected. The TC technique overcomes this ob- and t because the systematic difference is removed. s stacle by including three collocated independent data- Nonetheless, being a measure of absolute error, «1 is sets [Xi (i 2 {1, 2, 3})]. Without the knowledge of the sensitive to data variability and cannot be compared ground truth t, TC can estimate the standard deviation fairly across space and time; thus, we used r2 to assess t,X1 2 of random errors s« and coefﬁcients of determination representativeness. Note that r reﬂects the joint i t,X1 r2 of the linear regression model that predicts t with X . impacts of instrumental performance and spatial rep- t,Xi i 2 When X represents the point-scale dataset, s« and r resentativeness. Since snow depth observations of me- 1 1 t,X1 represent the accuracy of predicting the ground truth teorological stations are made manually, we can assume using point-scale dataset. If X1 is of limited spatial rep- that the instrumental error is negligible. However, for resentativeness for the coarse-scale, which is the spatial automatic sensors, the instrumental errors can be high measurement support for both X2 and X3, then the due to miscalibration or bad deployment (Gruber et al. prediction accuracy of X1 will be low because TC favors 2013); therefore, data quality of the automatic sensors

TABLE 2. Correlation coefﬁcients among variables. Strong correlations (jrj . 0.4) are shown in bold.

r2 for r2 for t,X1 t,X1 vPsnow mPland vPland mFsnow vFsnow mFland vFland TI MFC Mean_SD stable unstable mPsnow 20.76 0.09 0.14 0.35 20.46 20.06 20.61 20.75 20.70 20.24 0.06 20.19 vPsnow 0.00 20.10 20.30 0.55 0.06 0.54 0.77 0.65 0.17 20.20 0.10 mPland 20.39 20.31 20.37 0.52 20.14 20.04 20.17 20.37 20.12 20.08 vPland 20.12 20.03 20.03 0.52 20.19 20.02 20.16 20.09 20.18 mFsnow 0.48 20.84 20.45 20.18 0.00 0.68 0.44 0.51 vFsnow 20.67 0.33 0.50 0.70 0.75 0.25 0.39 mFland 0.12 20.03 20.26 20.82 20.40 20.49 vFland 0.36 0.56 0.04 20.17 20.02 TI 0.66 0.20 20.20 0.03 MFC 0.46 0.07 0.30 Mean_SD 0.44 0.62

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC APRIL 2020 W A N G A N D Z H E N G 801 should be checked carefully before using r2 to assess explanatory variables and the reduction in r2 .We t,X1 t,X1 spatial representativeness. found that mean_SD has the largest impact on seasonal variations (r 520.48). The smaller the annual mean b. Relating representativeness to spatially explicit snow depth is, the larger the seasonal variations are. variables Thus, when the time changes from the stable to the Spatial representativeness of in situ snow depth unstable period, many representative stations located in measurements is determined by the spatial variability of the southern region, where snow is usually shallower, snow depth in the surrounding area. Previous studies become nonrepresentative (Figs. 2b,c). We also found that evaluated the representativeness spatially modeled that stations with low forest cover in the surrounding the snow depth. This study omits spatial modeling, area tend to exhibit a large reduction in representa- which is infeasible for sparse networks, and directly as- tiveness (r 520.34), and terrain has a similar but sesses the representativeness of meteorological stations. weaker effect (r 520.26). For regions where forest Similar to the spatial pattern of snow depth shaped by a cover is low or terrain is flat, high wind speed or strong range of different processes that occur across a hierarchy radiation often occurs during the snow ablation season, of spatial scales (Trujillo et al. 2007; Jost et al. 2007; which can easily lead to patchy or heterogeneous snow Clark et al. 2011; Melvold and Skaugen 2013), repre- distributions. By contrast, snow distribution can be quite sentativeness distribution also reveals a smooth climate homogeneous during the snow accumulation period for pattern with additional local variations. After removing these regions. Therefore, when using stations in less the climate pattern, local variations in representative- forested regions or in flat regions for validation, their ness can be best explained by mPsnow (inconsistency in time-variant representativeness should be considered. snow cover presence between a station and its sur- d. Comparison of two coarse-scale snow depth roundings) and TI (terrain heterogeneity in the sur- products rounding area). This result agrees with the common knowledge that a point-scale dataset is less likely to be The TC-derived representativeness assessments are representative in heterogeneous regions; thus, it pro- impacted by the quality of two coarse-scale snow depth vides an indirect proof that the TC-derived representa- products (GlobSnow, CMC) used in this study. If there is tiveness assessment in this study is reasonable. no significant positive correlation between the two The relationship uncovered also highlights the ne- products, TC analysis cannot be carried out. If the two cessity of designing variables more pertinent to the products are both strongly correlated with the underly- heterogeneity of snow depth in explaining representa- ing ground truth, the representativeness results will be tiveness. Specifically, long time series snow cover data more credible. To better understand the coarse-scale should be explored fully to describe the snow cover data quality, we calculated pixel-wise Pearson correla- pattern, which is indicative of the snow depth pattern to tion coefficients Ri,j between GlobSnow and CMC based some extent. In future work, different sizes of window on the snow depth anomaly time series. The correlation region can be selected to explore the scaling effect of coefficient Ri,j depicts the consistency in temporal vari- snow cover heterogeneity around stations because this ations between the two datasets. Under the framework study only extracted explanatory variables from a win- of TC, Ri,j can also be written as follows (Gruber dow region with a fixed size. Furthermore, future work et al. 2016a): could use gap filling and smoothing techniques to im- Q b s b s 5 qffiffiffiffiffiffiffiffiffiffiffiffiffiij 5 piffiffiffiffiffiffiffit qjffiffiffiffiffiffiffit 5 r r prove the snow cover data quality so that snow clima- Ri,j t,X t,X . (19) Q i j tology features are more accurate. QiiQjj ii Qjj c. Understanding seasonal variations in Equation (19) shows that R is determined by the representativeness i,j multiplication of the correlation coefficients of the two

Our results conﬁrm that representativeness of a sta- products (Xi, Xj) with the ‘‘ground truth’’ (t). High Ri,j tion shows large seasonal variations. Since r2 is posi- values mean that both products are of high quality, while t,X1 tively correlated with snow depth, almost all stations low Ri,j values indicate that at least one product is not of have better representativeness during the stable period high quality. Figure 4 shows the Ri,j maps for three pe- when snow is deeper. Although most stations suffer re- riods (stable, unstable, and entire period). During the ductions in r2 when the time changes from the stable stable period, R values are high for most areas, al- t,X1 i,j to the unstable period, the magnitudes are different. though there is a belt of low values in the southern area To understand the factors that affect the magnitudes, (near the coastal region). During the unstable period, we calculated the correlation coefﬁcients between Ri,j values are much lower in the northern and eastern

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 802 JOURNAL OF HYDROMETEOROLOGY VOLUME 21

FIG. 4. Correlation coefﬁcients between GlobSnow and CMC snow depth anomaly time series for the (a) stable period, (b) unstable period, and (c) entire period.

mountainous areas, and the southern area still exhibits respect to satellite gridscale data for hundreds of me- the lowest values across the region. For the entire time teorological stations. By choosing the spatial repre- period, R shows the medium values, and its spatial sentative stations (r2 $ 0:5), validation work can be i,j t,X1 pattern reﬂects the combined effect in both stable and extended from a few core validation sites to widespread unstable periods. These results indicate that the quality sparse networks. The correlation metric should be of the two coarse-scale snow depth products varies adopted to validate new coarse-scale snow depth data with space and time. For regions with lower Ri,j values, because large systematic biases may still exist for those the representativeness results may have higher uncer- representative stations. The seasonality in the TC-derived tainties because at least one of the coarse-scale snow representativeness highlights the necessity of choosing the depth products is not strongly correlated with the ground best stations according to the time period of the products truth. Future studies should focus on these regions and under consideration. Representativeness assessments attempt to decrease the uncertainties in the representa- were indirectly proved to be reasonable by the close tiveness assessments by introducing new datasets or car- relationship between the two variables depicting het- rying out snow surveys. erogeneity features (mPsnow and TI) and the representativeness metric r2 . Despite its advantages, TC t,X1 cannot output the correct results when the three collo- 6. Conclusions cated datasets are not accurate enough or have high This study demonstrates that the TC technique is capable levels of error correlations. In the future, more mutually of efﬁciently and effectively evaluating the spatial repre- independent snow depth products of high quality should sentativeness of point-scale snow depth measurements with be used to extend TC to an arbitrary number of datasets

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC APRIL 2020 W A N G A N D Z H E N G 803 and to increase the robustness and accuracy of the rep- (SMAP) level 2 data products. IEEE J. Sel. Top. Appl. resentativeness evaluation. Snow surveys around the Earth Obs. Remote Sens., 10, 489–502, https://doi.org/10.1109/ stations should also be performed to provide a bench- JSTARS.2016.2569998. Clark, M. P., and Coauthors, 2011: Representing spatial variability mark for directly evaluating the TC approach. of snow water equivalent in hydrologic and land-surface models: A review. Water Resour. Res., 47, W07539, https:// Acknowledgments. This research is funded by the doi.org/10.1029/2011WR010745. National Key Research and Development Program of Cohen, J., 1994: Snow cover and climate. Weather, 49, 150–156, China (2018YFC1506605; 2018YFC1506501) and Science https://doi.org/10.1002/j.1477-8696.1994.tb05997.x. Dai, L. Y., and T. Che, 2011: Spatiotemporal distributions and in- and Technology Basic Resources Investigation Program of fluences on snow density in China from 1999 to 2008. Sci. Cold China (2017FY100500). Arid. Reg., 4, 325–331. Deems, J. S., S. R. Fassnacht, and K. J. Elder, 2008: Interannual consistency in fractal snow depth patterns at two Colorado REFERENCES mountain sites. J. Hydrometeor., 9, 977–988, https://doi.org/ Armstrong, R., and M. Brodzik, 2002: Hemispheric-scale com- 10.1175/2008JHM901.1. parison and evaluation of passive-microwave snow algo- Derksen, C., A. Walker, and B. Goodison, 2003: A comparison of rithms. Ann. Glaciol., 34, 38–44, https://doi.org/10.3189/ 18 winter seasons of in situ and passive microwave-derived 172756402781817428. snow water equivalent estimates in western Canada. Remote Berezowski, T., J. Chormanski, and O. Batelaan, 2015: Skill of Sens. Environ., 88, 271–282, https://doi.org/10.1016/ remote sensing snow products for distributed runoff pre- j.rse.2003.07.003. diction. J. Hydrol., 524, 718–732, https://doi.org/10.1016/ Dong, C., and L. Menzel, 2016: Producing cloud-free MODIS snow j.jhydrol.2015.03.025. cover products with conditional probability interpolation and Blöschl, G., 1999: Scaling issues in snow hydrology. Hydrol. meteorological data. Remote Sens. Environ., 186, 439–451, Processes, 13, 2149–2175, https://doi.org/10.1002/(SICI)1099- https://doi.org/10.1016/j.rse.2016.09.019. 1085(199910)13:14/15,2149::AID-HYP847.3.0.CO;2-8. Dorigo, W. A., K. Scipal, R. M. Parinussa, Y. Y. Liu, W. Wagner, Bohnenstengel, S. I., K. H. Schlünzen, and F. Beyrich, 2011: R. A. M. de Jeu, and V. Naeimi, 2010: Error characterisation Representativity of in situ precipitation measurements – A case of global active and passive microwave soil moisture datasets. study for the LITFASS area in North-Eastern Germany. J. Hydrol., Hydrol. Earth Syst. Sci., 14, 2605–2616, https://doi.org/10.5194/ 400, 387–395, https://doi.org/10.1016/j.jhydrol.2011.01.052. hess-14-2605-2010. Bormann, K. J., M. F. McCabe, and J. P. Evans, 2012: Satellite ——, and Coauthors, 2015: Evaluation of the ESA CCI soil based observations for seasonal snow cover detection and moisture product using ground-based observations. Remote characterisation in Australia. Remote Sens. Environ., 123, Sens. Environ., 162, 380–395, https://doi.org/10.1016/ 57–71, https://doi.org/10.1016/j.rse.2012.03.003. j.rse.2014.07.023. Brasnett, B., 1999: A global analysis of snow depth for numerical Draper, C., R. Reichle, R. de Jeu, V. Naeimi, R. Parinussa, and weather prediction. J. Appl. Meteor., 38, 726–740, https://doi.org/ W. Wagner, 2013: Estimating root mean square errors in re- 10.1175/1520-0450(1999)038,0726:AGAOSD.2.0.CO;2. motely sensed soil moisture over continentalscale domains. Brown, R. D., and B. Brasnett, 2010: Canadian Meteorological Remote Sens. Environ., 137, 288–298, https://doi.org/10.1016/ Centre (CMC) daily snow depth analysis data, version 1. j.rse.2013.06.013. NASA National Snow and Ice Data Center Distributed Foster, J. L., D. K. Hall, J. B. Eylander, G. A. Riggs, S. V. Nghiem, Active Archive Center, accessed 8 October 2019, https://doi.org/ M. Tedesco, and B. Choudhury, 2011: A blended global snow 10.5067/W9FOYWH0EQZ3. product using visible, passive microwave and scatterometer Chang, A. T. C., and A. Rango, 2000: Algorithm Theoretical Basis satellite data. Int. J. Remote Sens., 32, 1371–1395, https:// Document (ATBD) for the AMSR-E snow water equivalent doi.org/10.1080/01431160903548013. algorithm, version 3.1. NASA Goddard Space Flight Center, Gruber, A., W. Dorigo, S. Zwieback, A. Xaver, and W. Wagner, 49 pp., https://nsidc.org/sites/nsidc.org/files/technical-references/ 2013: Characterizing coarse-scale representativeness of in situ amsr_atbd_snow.pdf. soil moisture measurements from the international soil mois- ——, J. L. Foster, and D. K. Hall, 1996: Effects of forest on the snow ture network. Vadose Zone J., 12, 1–16, https://doi.org/ parameters derived from microwave measurements during the 10.2136/vzj2012.0170. Boreas winter field campaign. Hydrol. Processes, 10, 1565–1574, ——,C.-H.Su,S.Zwieback,W.T.Crow,W.Dorigo,and https://doi.org/10.1002/(SICI)1099-1085(199612)10:12,1565:: W. Wagner, 2016a: Recent advances in (soil moisture) triple AID-HYP501.3.0.CO;2-5. collocation analysis. Int. J. Appl. Earth Obs. Geoinf., 45, ——, R. E. J. Kelly, E. G. Josberger, R. L. Armstrong, J. L. Foster, 200–211, https://doi.org/10.1016/J.JAG.2015.09.002. and N. M. Mognard, 2005: Analysis of ground-measured and ——, ——, W. T. Crow, S. Zwieback, W. A. Dorigo, and W. Wagner, passive-microwave-derived snow depth variations in midwin- 2016b: Estimating error cross-correlation in soil moisture data ter across the northern great plains. J. Hydrometeor., 6, 20–33, sets using extended collocation analysis. J. Geophys. Res. https://doi.org/10.1175/JHM-405.1. Atmos., 121, 1208–1219, https://doi.org/10.1002/2015JD024027. Che,T.,L.Dai,X.Zheng,X.Li,andK.Zhao,2016:Estimationof ——, W. A. Dorigo, W. Crow, and W. Wagner, 2017: Triple snow depth from passive microwave brightness temperature collocation-based merging of satellite soil moisture retrievals. data in forest regions of northeast China. Remote Sens. IEEE Trans. Geosci. Remote Sens., 55, 6780–6792, https:// Environ., 183, 334–349, https://doi.org/10.1016/j.rse.2016.06.005. doi.org/10.1109/TGRS.2017.2734070. Chen, F., and Coauthors, 2017: Application of triple collocation Grünewald, T., and M. Lehning, 2013: Can a point measurement in ground-based validation of Soil Moisture Active/Passive represent the snow depth in its vicinity? A comparison of areal

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 804 JOURNAL OF HYDROMETEOROLOGY VOLUME 21

snow depth measurements with selected index sites. Int. Snow ——, and ——, 2006: SNOTEL representativeness in the Rio Science Workshop 2013, Grenoble, France, ISSW, 69–72, Grande headwaters on the basis of physiographics and re- https://arc.lib.montana.edu/snow-science/item/1952. motely sensed snow cover persistence. Hydrol. Processes, 20, ——, and Coauthors, 2013: Statistical modelling of the snow depth 723–739, https://doi.org/10.1002/hyp.6128. distribution in open alpine terrain. Hydrol. Earth Syst. Sci., 17, Neumann, N. N., C. Derksen, C. Smith, and B. Goodison, 2006: 3005–3021, https://doi.org/10.5194/hess-17-3005-2013. Characterizing local scale snow cover using point measure- Hall, D. K., and G. A. Riggs, 2007: Accuracy assessment of the ments during the winter season. Atmos.–Ocean, 44, 257–269, MODIS snow products. Hydrol. Processes, 21, 1534–1547, https://doi.org/10.3137/ao.440304. https://doi.org/10.1002/hyp.6715. Nitta, T., and Coauthors, 2014: Representing variability in subgrid Hansen, M. C., R. S. DeFries, J. R. G. Townshend, L. Marufu, and snow cover and snow depth in a global land model: Offline R. Sohlberg, 2002: Development of a MODIS tree cover val- validation. J. Climate, 27, 3318–3330, https://doi.org/10.1175/ idation data set for western province, Zambia. Remote Sens. JCLI-D-13-00310.1. Environ., 83, 320–335, https://doi.org/10.1016/S0034-4257(02) Pulliainen, J., 2006: Mapping of snow water equivalent and snow 00080-9. depth in boreal and sub-arctic zones by assimilating space- He, W., R. C. Bu, Z. P. Xiong, and Y. M. Hu, 2013: Characteristics borne microwave radiometer data andground-based obser- of temperature and precipitation in Northeastern China from vations. Remote Sens. Environ., 101, 257–269, https://doi.org/ 1961 to 2005. Acta Ecol. Sin., 33, 519–531, https://doi.org/ 10.1016/j.rse.2006.01.002. 10.5846/stxb201111241799. Raleigh, M. S., K. Rittger, C. E. Moore, B. Henn, J. A. Lutz, and Jost, G., M. Weiler, D. R. Gluns, and Y. Alila, 2007: The influence J. D. Lundquist, 2013: Ground-based testing of MODIS frac- of forest and topography on snow accumulation and melt at tional snow cover in subalpine meadows and forests of the the watershed-scale. J. Hydrol., 347, 101–115, https://doi.org/ Sierra Nevada. Remote Sens. Environ., 128, 44–57, https:// 10.1016/j.jhydrol.2007.09.006. doi.org/10.1016/j.rse.2012.09.016. Li, X., and Coauthors, 2008: Cryospheric change in China. Rice, R., and R. C. Bales, 2010: Embedded-sensor network design Global Planet. Change, 62, 210–218, https://doi.org/10.1016/ for snow cover measurements around snow pillow and snow j.gloplacha.2008.02.001. course sites in the Sierra Nevada of California. Water Resour. Liston, G. E., 1999: Interrelationships among snow distribution, Res., 46, W03537, https://doi.org/10.1029/2008WR007318. snowmelt, and snow cover depletion: Implications for atmo- Schirmer, M., V. Wirz, A. Clifton, and M. Lehning, 2011: Persistence spheric, hydrologic, and ecologic modeling. J. Appl. Meteor., in intra-annual snow depth distribution: 1. Measurements and 38, 1474–1487, https://doi.org/10.1175/1520-0450(1999) topographic control. Water Resour. Res., 47,W09516,https:// 038,1474:IASDSA.2.0.CO;2. doi.org/10.1029/2010WR009426. ——, 2004: Representing subgrid snow cover heterogeneities in Scipal, K., T. Holmes, R. de Jeu, V. Naeimi, and W. Wagner, 2008: regional and global models. J. Climate, 17, 1381–1397, A possible solution for the problem of estimating the error https://doi.org/10.1175/1520-0442(2004)017,1381:RSSCHI. structure of global soil moisture data sets. Geophys. Res. Lett., 2.0.CO;2. 35, L24403, https://doi.org/10.1029/2008GL035599. Loew, A., and F. Schlenz, 2011: A dynamic approach for evaluating Stoffelen, A., 1998: Toward the true near-surface wind speed: Error coarse scale satellite soil moisture products. Hydrol. Earth modeling and calibration using triple collocation. J. Geophys. Syst. Sci., 15, 75–90, https://doi.org/10.5194/hess-15-75-2011. Res., 103, 7755–7766, https://doi.org/10.1029/97JC03180. Maurer, E. P., J. D. Rhoads, R. O. Dubayah, and D. P. Lettenmaier, Stroeve, J., J. E. Box, F. Gao, S. Liang, A. Nolin, and C. Schaaf, 2003: Evaluation of the snowcovered area data product from 2005: Accuracy assessment of the MODIS 16-day albedo MODIS. Hydrol. Processes, 17, 59–71, https://doi.org/10.1002/ product for snow: Comparisons with Greenland in situ mea- hyp.1193. surements. Remote Sens. Environ., 94, 46–60, https://doi.org/ McColl, K. A., J. Vogelzang, A. G. Konings, D. Entekhabi, 10.1016/j.rse.2004.09.001. M. Piles, and A. Stoffelen, 2014: Extended triple collocation: Sturm, M., J. Holmgren, and G. Liston, 1995: A seasonal snow Estimating errors and correlation coefficients with respect to cover classification system for local to global applications. an unknown target. Geophys. Res. Lett., 41, 6229–6236, https:// J. Climate, 8, 1261–1283, https://doi.org/10.1175/1520- doi.org/10.1002/2014GL061322. 0442(1995)008,1261:ASSCCS.2.0.CO;2. Melvold, K., and T. Skaugen, 2013: Multiscale spatial variability of Takala, M., K. Luojus, J. Pulliainen, C. Derksen, J. Lemmetyinen, lidar-derived and modeled snow depth on Hardangervidda, J. Kärnä, J. Koskinen, and B. Bojkov, 2011: Estimating Norway. Ann. Glaciol., 54, 273–281, https://doi.org/10.3189/ northern hemisphere snow water equivalent for climate re- 2013AoG62A161. search through assimilation of space-borne radiometer data Meromy,L.,N.P.Molotch,T.E.Link,S.R.Fassnacht,and and ground-based measurements. Remote Sens. Environ., 115, R. Rice, 2013: Subgrid variability of snow water equiva- 3517–3529, https://doi.org/10.1016/j.rse.2011.08.014. lent at operational snow stations in the western USA. Trujillo, E., J. A. Ramírez, and K. J. Elder, 2007: Topographic, Hydrol. Processes, 27, 2383–2400, https://doi.org/10.1002/ meteorologic, and canopy controls on the scaling charac- hyp.9355. teristics of the spatial distribution of snow depth fields. Miralles, D. G., W. T. Crow, and M. H. Cosh, 2010: Estimating Water Resour. Res., 43, W07409, https://doi.org/10.1029/ spatial sampling errors in coarse-scale soil moisture estimates 2006WR005317. derived from point-scale observations. J. Hydrometeor., 11, Tustison, B., D. Harris, and E. Foufoula-Georgiou, 2001: 1423–1429, https://doi.org/10.1175/2010JHM1285.1. Scale issues in verification of precipitation forecasts. Molotch, N. P., and R. C. Bales, 2005: Scaling snow observations J. Geophys. Res., 106, 11 775–11 784, https://doi.org/10.1029/ from the point to the grid element: Implications for observa- 2001JD900066. tion network design. Water Resour. Res., 41, W11421, https:// Vander Jagt, B. J., M. T. Durand, S. A. Margulis, E. J. Kim, and doi.org/10.1029/2005WR004229. N. P. Molotch, 2013: The effect of spatial variability on the

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC APRIL 2020 W A N G A N D Z H E N G 805

sensitivity of passive microwave measurements to snow water Yilmaz, M. T., and W. T. Crow, 2014: Evaluation of as- equivalent. Remote Sens. Environ., 136, 163–179, https:// sumptions in soil moisture triple collocation analysis. doi.org/10.1016/j.rse.2013.05.002. J. Hydrometeor., 15, 1293–1302, https://doi.org/10.1175/ Vanderlinden, K., H. Vereecken, H. Hardelauf, M. Herbst, G. Martínez, JHM-D-13-0158.1. M. H. Cosh, and Y. A. Pachepsky, 2012: Temporal stability of soil Zhang, D. W., Z. T. Cong, and G. H. Ni, 2016: Snowfall changes in water contents: A review of data and analyses. Vadose Zone J., 11, China during 1956-2010. Qinghua Daxue Xuebao Ziran vzj20110178, https://doi.org/10.2136/vzj2011.0178. Kexueban, 56, 381–386, 393. Winstral, A., and D. Marks, 2014: Long-term snow distribution ob- Zwieback, S., K. Scipal, W. Dorigo, and W. Wagner, 2012: Structural servations in a mountain catchment: Assessing variability, time and statistical properties of the collocation technique for error stability, and the representativeness of an index site. Water characterization. Nonlinear Processes Geophys., 19, 69–80, Resour. Res., 50, 293–305, https://doi.org/10.1002/2012WR013038. https://doi.org/10.5194/npg-19-69-2012.

Unauthenticated | Downloaded 10/05/21 12:39 PM UTC