Spatial Representativeness Analysis for Snow Depth Measurements of Meteorological Stations in Northeast China
Total Page：16
File Type：pdf, Size：1020Kb
APRIL 2020 W A N G A N D Z H E N G 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 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 ob- tain 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 corre- lation 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 mois- ture 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.