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

<ul style="display: flex;"><li style="flex:1">APRIL 2020 </li><li style="flex:1">W A N G A N D Z H E N G </li></ul>791 Spatial Representativeness Analysis for Snow Depth Measurements of Meteorological Stations in Northeast China 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 r2t,X estimated with TC. Stations are 1considered representative if r2t,X $ 0:5; that is, in situ measurements explain no less than 50% of the variations 1in 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 r2t,X values, of which 57 stations are 1representative for the entire snow season (October–December, January–April). 2) Seasonal variations in rt2,X 1are 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 r2t,X is positively correlated with mean snow depth, which largely determines the global decreasing 1trend in r2t,X from north to south. After removing this trend, residuals in r2t,X can be explained by heterogeneity features concerning elevation and conditional probability of snow presence near the stations. <ul style="display: flex;"><li style="flex:1">1</li><li style="flex:1">1</li></ul>1. Introduction Validation of microwave snow depth products with ground truth data is key to improving inversion algorithms. However, owing to the high spatial variability of snow depth, the validation process can be quite challenging. An in situ snow depth measurement can only be representative over a very small spatial scale (Clark et al. 2011; Trujillo et al. 2007), whereas satellite-derived snow depth represents the mean value of a microwave footprint with a size of 25 km 3 25 km or larger (Vander Jagt et al. 2013). If satellitederived snow depth is directly compared with point measurements, the obtained errors are likely dominated by representativeness errors due to the variability of the snow depth field on subgrid scales as opposed to snow depth inversion model errors (Brasnett 1999; Tustison et al. 2001; Chang et al. 2005; Liston 1999, 2004). Snow cover is a key component in the global water cycle and directly impacts the Earth’s energy balance and climate dynamics (Cohen 1994). Remote sensing is the most efficient way to regularly measure snow cover and depth on global and regional scales (Armstrong and Brodzik 2002; Foster et al. 2011). The Scanning Multichannel Microwave Radiometer (SMMR), Special Sensor Microwave Imager (SSM/I), and Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) have been routinely used to retrieve snow depth and snow water equivalent (SWE) since the 1970s (Che et al. 2016). Satellite snow products are increasingly used for modeling and monitoring in various fields such as hydrology (Berezowski et al. 2015), climate research (Bormann et al. 2012), glaciology (Stroeve et al. 2005), and numerical weather prediction (Brasnett 1999). To evaluate the spatial representativeness of the point-scale snow depth, most studies attempted to obtain the difference between the point measurement and the area average, and argued that a point measurement is representative if its value deviates less than Corresponding author: Yuanyuan Wang, <a href="mailto:[email protected]" target="_blank">wangyuany@ </a><a href="mailto:[email protected]" target="_blank">cma.gov.cn </a>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 <a href="/goto?url=http://www.ametsoc.org/PUBSReuseLicenses" target="_blank">AMS Copyright </a><a href="/goto?url=http://www.ametsoc.org/PUBSReuseLicenses" target="_blank">Policy </a>(<a href="/goto?url=http://www.ametsoc.org/PUBSReuseLicenses" target="_blank">www.ametsoc.org/PUBSReuseLicenses</a>). Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 792 J O U R N A L O F H Y D R O M E T E O R O L O G Y 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 successthe snow ablation period owing to the variafully 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 obserin 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 opor the ablation season process (Molotch and erational meteorological stations, the limitations of Bales 2005). Understanding the seasonal variapoint 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 advanof 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 compreable if they are strongly correlated with heterohensive 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 pointfor new sites. scale and two coarse-scale datasets that have the similar <ul style="display: flex;"><li style="flex:1">spatial resolution, performance metrics associated with </li><li style="flex:1">The remainder of this paper is organized as follows. </li></ul>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 feathe 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 the closeness of the point-scale data to the coarse-scale 2. Introduction of the TC technique a. TC approaches ground truth has been confirmed at densely instrumented validation sites by Miralles et al. (2010) and Chen et al. (2017). The most commonly used error model for TC analysis 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 TC applications in soil moisture studies has prompted Xi 5 ai 1 bit 1 «i , (1) us to adopt this technique for snow depth studies. where Xi (i 2 {1, 2, 3}) are three collocated and indeTo the best of our knowledge, this study is the first at- pendent datasets of the same geophysical variable linetempt 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. The terms Xi, 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 <ul style="display: flex;"><li style="flex:1">APRIL 2020 </li><li style="flex:1">W A N G A N D Z H E N G </li></ul>793 (6) 8Q12Q13 Q23 and multiplicative biases of dataset Xi with respect to the true signal t. 2«>>>s5 Q11 2221>>>>There are four main underlying assumptions for the error model of TC (Zwieback et al. 2012; Gruber et al. 2016a,b): (i) linearity between the true signal and the observations; (ii) signal and error stationarity; (iii) error orthogonality: independence between the errors and the true signal, that is, Cov(t, «i) 5 0; and (iv) zero error cross correlation: independence between the errors of Xi and Xj, that is, Cov(«i, «j) 5 0, for i ¼ j. >><Q12Q23 Q13 s2« 5 Q22 .2>>>>>>>>>:Q13Q23 Q12 2s« 5 Q33 3Since s2« is the absolute random error variance af- ifected by the dynamic range of the data, Draper et al. (2013) proposed relative error variance (fMSEi), which is calculated by normalizing the error variances with the corresponding dataset variances: Following McColl et al. (2014), the covariances between the different datasets are calculated as follows: Cov(Xi, Xj) 5 E(XiXj) 2 E(Xi)E(Xj) s«2 i5 bibjs2t 1 biCov(t, «j) 1 bjCov(t, «i) <ul style="display: flex;"><li style="flex:1">fMSEi 5 </li><li style="flex:1">.</li><li style="flex:1">(7) </li></ul>Qii 1 Cov(«i, «j), (2) Combining (7), (4), and (3), fMSEi can be written as follows: where s2t 5 var(t). Using the assumptions of error orthogonality and zero error cross correlation, the equation is reduced to (3): <ul style="display: flex;"><li style="flex:1">s«2 </li><li style="flex:1">s«2 </li></ul><ul style="display: flex;"><li style="flex:1">i</li><li style="flex:1">i</li></ul>fMSEi 5 5<ul style="display: flex;"><li style="flex:1">,</li><li style="flex:1">(8) </li></ul>u2i 1 s2« b2i st2 1 s2« <ul style="display: flex;"><li style="flex:1">i</li><li style="flex:1">i</li></ul>(bibjs2t , bibjs2t 1 s2« , for i 5 j for i ¼ j <ul style="display: flex;"><li style="flex:1">where b2i st2 represents the signal and s«2 represents the </li><li style="flex:1">Qij [ Cov(Xi, Xj) 5 </li><li style="flex:1">,</li><li style="flex:1">(3) </li></ul>inoise (Gruber et al. 2016a; McColl et al. 2014); thus, fMSEi is not only a measure of relative error, but also a measure of signal-to-noise ratio (SNR). Furthermore, fMSEi is related to the linear correlation coefficient of iwhere s2« 5 var(«i), representing the variance of irandom error in dataset Xi. Since there are six equations (Q11, Q12, Q13, Q22, Q23, Q33) but seven unknowns (b1, b2, b3, s« , s« , s« , st), the system is Xi with the underlying true signal t (denoted by rt,X ). According to McColl et al. (2014), the relationship be- i<ul style="display: flex;"><li style="flex:1">1</li><li style="flex:1">2</li><li style="flex:1">3</li></ul>underdetermined. It can be solved by defining a new variable ui 5 bist. Then, the equations can be rewritten as in (4): tween rt,X and the ordinary least squares (OLS) slope bi can be written as in (9): i(bist pffiffiffiffiffiffi uiuj, for i ¼ j rt,X 5<ul style="display: flex;"><li style="flex:1">.</li><li style="flex:1">(9) </li></ul>iQii Qij 5 <ul style="display: flex;"><li style="flex:1">.</li><li style="flex:1">(4) </li></ul>u2i 1 s2« , for i 5 j iCombining (7), (8), and (9), we obtain (10): Now there are six equations and six unknowns, and the system can be solved. Variable u2i , which provides estimates of the sensitivity of datasets Xi to ground truth changes (Gruber et al. 2016a), can be written as follows: Qii 2 s2« s«2 b2i s2t r2t,X <ul style="display: flex;"><li style="flex:1">5</li><li style="flex:1">5</li></ul>i 5 1 2 i 5 1 2 fMSEi . (10) i<ul style="display: flex;"><li style="flex:1">Qii </li><li style="flex:1">Qii </li><li style="flex:1">Qii </li></ul>Equation (10) indicates that r2t,X and fMSEi are 8Q12Q13 i21 21 2t>>>u 5 b s 5 complementary. When fMSEi is 0.5, the coefficient of determination r2t,X for the linear error model is 0.5, and Q23 >>>>i<ul style="display: flex;"><li style="flex:1">pffiffiffiffiffiffi </li><li style="flex:1">></li></ul>><the correlation coefficient of Xi with t is 0:5 (’0.71). Q12Q23 Q13 u22 5 b22s2t 5 <ul style="display: flex;"><li style="flex:1">.</li><li style="flex:1">(5) </li></ul>>>b. Representativeness analysis of point-scale data with TC >>>>>>>:Q13Q23 Q12 <ul style="display: flex;"><li style="flex:1">2</li><li style="flex:1">2</li><li style="flex:1">2</li></ul>u3 5 b3st 5 While TC is a powerful tool for estimating random errors and removing systematic differences between the The estimation equation for error variances can be signal variance component of observations, it is affected <ul style="display: flex;"><li style="flex:1">written as follows: </li><li style="flex:1">by representativeness errors (Yilmaz and Crow 2014). </li></ul>Unauthenticated | Downloaded 10/05/21 12:39 PM UTC 794 J O U R N A L O F H Y D R O M E T E O R O L O G Y 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-

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

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