Representativeness of the ground observational sites and up-scaling of the point soil moisture measurements

Journal of Hydrology 533 (2016) 62–73

Contents lists available at ScienceDirect

Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol

Representativeness of the ground observational sites and up-scaling of the point soil moisture measurements Jinlei Chen a,b, Jun Wen a,⇑, Hui Tian a a Key Laboratory of Land Surface Process and Climate Change in Cold and Arid Regions, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China b University of Chinese Academy of Sciences, Beijing 100049, China

a r t i c l e

i n f o

Article history: Received 7 May 2015 Received in revised form 20 July 2015 Accepted 24 November 2015 Available online 6 December 2015 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Venkat Lakshmi, Associate Editor Keywords: Soil moisture Up-scaling Time stability analysis Sliding correlation analysis

s u m m a r y Soil moisture plays an increasingly important role in the cycle of energy–water exchange, climate change, and hydrologic processes. It is usually measured at a point site, but regional soil moisture is essential for validating remote sensing products and numerical modeling results. In the study reported in this paper, the minimal number of required sites (NRS) for establishing a research observational network and the representative single sites for regional soil moisture estimation are discussed using the soil moisture data derived from the ‘‘Maqu soil moisture observational network” (101°400 –102°400 E, 33°300 –35°450 N), which is supported by Chinese Academy of Science. Furthermore, the best up-scaling method suitable for this network has been studied by evaluating four commonly used up-scaling methods. The results showed that (1) Under a given accuracy requirement R P 0.99, RMSD 6 0.02 m3/m3, NRS at both 5 and 10 cm depth is 10. (2) Representativeness of the sites has been validated by time stability analysis (TSA), time sliding correlation analysis (TSCA) and optimal combination of sites (OCS). NST01 is the most representative site at 5 cm depth for the first two methods; NST07 and NST02 are the most representative sites at 10 cm depth. The optimum combination sites at 5 cm depth are NST01, NST02, and NST07. NST05, NST08, and NST13 are the best group at 10 cm depth. (3) Linear fitting, compared with other three methods, is the best up-scaling method for all types of representative sites obtained above, and linear regression equations between a single site and regional soil moisture are established hereafter. ‘‘Single site” obtained by OCS has the greatest up-scaling effect, and TSCA takes the second place. (4) Linear fitting equations show good practicability in estimating the variation of regional soil moisture from July 3, 2013 to July 3, 2014, when a large number of observed soil moisture data are lost. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Soil moisture is closely linked to the local precipitation and evapotranspiration, which has great significance in the study of energy–water exchange between land and atmosphere (Bian et al., 2012; Wang et al., 2008). Consequently, it plays an increasingly important role in climate change and hydrologic processes (Ma et al., 2001; Wei et al., 2000) and to this end, a series of studies have been carried out. In climate change area, scientists found that the role of soil moisture only ranks second to sea surface temperature (Wen et al., 2003) and it has a significant effect upon the global water cycle (Hong and Pan, 2000), because of its strong positive correlation to precipitation. In the study of land surface hydrologic ⇑ Corresponding author at: 320# Donggang West Road, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China. Tel.: +86 931 4967666 (O); fax: +86 931 4967666. E-mail address: [email protected] (J. Wen). http://dx.doi.org/10.1016/j.jhydrol.2015.11.032 0022-1694/Ó 2015 Elsevier B.V. All rights reserved.

processes, soil moisture is known as ‘‘impounding reservoir” in land surface water cycle, which effectively controls the distribution of local precipitation through land surface evapotranspiration, surface runoff, infiltration, and then affects water resources holistically (Liu et al., 2004; Sun et al., 2001). In agriculture, soil moisture numerically denotes water content and can be used to estimate grain yield, drought, etc. (Zhang et al., 2004). The factors that impact soil moisture include soil texture, terrain, vegetation, and weather. The response of soil moisture to various climates has been investigated, and it is found that precipitation is the main climate factor for spatial heterogeneity of soil moisture (Crow et al., 2012). Soil moisture is obtained by four basic methods, ground observation, remote sensing, numerical simulation, and data assimilation. It can be more precise if it is measured by oven drying representative soil or probes at different depths; however, the small spatial samples qualify these techniques as limited scale research. Currently, various observational networks in different scales have

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

been established by institutes throughout the world (Crow et al., 2012; Dente et al., 2012; Robock et al., 2000; Yang et al., 2013). With the rapid development of remote sensing, the acquisition of soil moisture on a large scale has evolved and a series of inversion algorithms (Jung et al., 2010; Shi et al., 2006; Wen et al., 2005), which utilize visible and near-infrared information, or microwave radiation, have been widely employed, especially the method of passive and active microwave remote sensing. These developments portend a bountiful era for the exploration of global scale soil moisture as reflected by the implementation of several remote sensing missions. The most famous of these are the soil moisture and ocean salinity (SMOS) mission (Kerr et al., 2001) and the soil moisture active–passive (SMAP) mission (Entekhabi et al., 2010). However, satellite remote sensing only sense top-layer soil moisture at a few centimeters depths (Crow et al., 2012). In fact, climate change is closely related to deep layers soil water content. Land surface models have an advantage in simulation of soil moisture at different depths, which is accompanied by a large uncertainty, because of its dependence on parameterization schemes of physical mechanisms and forcing data. Taken in total, the methods mentioned above have their respective pros and cons. Data assimilation fuses all of these data together and attempts to produce better temporal or spatial soil moisture data. Although the last three methods have potential to obtain global scale soil moisture, they still require surface observation as verification. Due to the spatial heterogeneity of soil moisture, the observation of single site has circumscribed representativeness. This approach is unable to provide the ‘‘ground truth” to validate the results obtained by remote sensing, land surface modeling or climate and hydrological modeling, owing to the poor resolution of remote sensing (AMSR-E  60 km2, SMOS  30–50 km2) and large grid interval of numerical simulation (Wen et al., 2003; De Lannoy et al., 2007). Consequently, the data observed from ground sites often have serious deficiencies causing further damage to spatial representativeness and refuting the initial objective of the network. The representative values vary from site to site, so one or several sites with high-quality values, which could denote the variation of soil moisture in this network, can be selected as representative sites, and others would be used to enrich the details. Therefore, it is vital to take care of these key sites in order to guarantee the spatial representativeness and historical comparability of time series. In conclusion, that using statistical methods to search the specific sampling core sites, and then obtain a true soil moisture on a regional scale by up-scaling these sites, has great significance in research and practical applications. It is not only potential for validating the results of remote sensing estimates and numerical simulations, but also reduce the maintenance cost of network. There are a variety of methods can be used to up-scaling the point soil moisture measurements to regional scale, mainly including four categories (Crow et al., 2012; Zhao et al., 2013). The first type of method based on TSA, which acquires one or several time-stable sites by statistical analysis of soil moisture between the point and average value. The value of time-stable site or mean value of several sites is what will be recognized as the regional soil moisture (Vachaud et al., 1985). The second approach uses a geostatistical algorithm to find the correlation structure, such as semivariogram of soil moisture measurements at different stations, which then will be used to compute the area averaged value (Vinnikov et al., 1999). The third strategy is based on intensive observation. A large number of sites are built to produce a considerable temporal and spatial database, finding the time-stable sites and constructing a linear regression relationship with averaged soil moisture measurements in this region (De Rosnay et al., 2009). The final method is to run a land surface model at a fine spatial resolution and then utilize the resulting spatial pattern of soil moisture to perform the up-scaling (Crow et al., 2005).

63

Based on this discussion and soil moisture profile data observed in ‘‘Maqu soil moisture observational network” (hereafter referred as Maqu SM-network), this investigation is mainly focused on the following three purposes. First, determining the number of required sites (NRS) which can be used to estimate the regional soil moisture in Maqu, and then seeking the most representative single site and selecting the best algorithm in four commonly used upscaling methods. In the next section, the study area and data will be described and the features of surface soil moisture changes will be concisely analyzed. Following this, the specific methods are introduced, including the random sampling–NRS analyses, time stability analysis, time sliding correlation analysis, OCS and several kinds of up-scaling methods. Then, using the methods previously mentioned to calculate and analyze the results, and these methods will be applied to determine the variation of soil moisture during 2013–2014 when the data are lost. Finally, conclusions of this study are summarized, drawbacks discussed, and further research is proposed. 2. Study area and datasets 2.1. General background of Maqu The study area of this investigation is concentrated in the region of Maqu county in Gansu province, China, which belongs to the upstream of Yellow River in the northwest part of the Tibet Plateau (101°400 –102°400 E, 33°300 –35°450 N), honored as ‘‘The First Turn of Yellow River”. The mean altitude here is about 3600 m above sea level (asl) and mean annual precipitation is 505 mm. Under the influence of the Tibetan Plateau and continental climate of the East Asian monsoon, winter drought and summer rains are the climatological characteristics in this area, and the mean annual temperature is 2 °C (Tian et al., 2011). The east part of the Maqu has flat terrain where is covered by short grasses, deteriorated grassland, swamps, meadow, and wetland, with the rest parts mainly composed by rugged mountains where capped with alpine meadow (Guo et al., 2009). 2.2. Maqu SM-network Maqu SM-network is located at a meso-scale scope (100 km  50 km) in the Gannan Tibetan Autonomous Prefecture (shown in Fig. 1) and contains 20 sampling sites distributed throughout the flat lands or on gentle slopes. Each site is equipped with ECH20 EC-TM which have been buried at depths of 5, 10, 20, 40, and 80 cm with a data logger box (ECH20-EM50) produced by Decagon Equipment, Inc. of Pullman, WA., USA. Resolution of the reader is 0.001 m3/m3, and data-logger records the variation of soil moisture and temperature in five layers within 12.6 months under the recording interval of 15 min. The data are corrected by using a soil moisture calibration curve that was constructed by sample oven drying method (Dente et al., 2012; Tian et al., 2011). In this study, soil moisture data during the period from July 1, 2011 to August 31, 2012 of two layers, 5 cm (including 15 sites, data in CST1, CST2, NST4, NST10, and NST15 are missing) and 10 cm (including 14 sites, data in CST1, CST2, NST4, NST10, NST12 and NST15 are lost), are used to analyze NRS, and look for the best up-scaling method, which is used to generate an annual estimate of regional soil moisture changes during 2013–2014. 2.3. The temporal variation of soil moisture Soil moisture is essential in the research of climatic and hydrological changes. As shown in Fig. 2a, daily variation of soil moisture from July, 2011 to August, 2012 is indicative of several other

64

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

Fig. 1. The geographic location and sites distribution of Maqu SM-network.

changes. Daily soil moisture presents a clear seasonal variation during the freeze–thawing process. Water content of soil decreases as water freezes in winter and increases during the late spring when ground starts thawing. That is because only the liquid water can be detected by our instruments, and climate in this region is dry and less rainfall in winter but rainy in summer. Furthermore, soil moisture is significantly correlated with precipitation (data provided by the ECMWF). Snow is solid precitation for an extended period and even when melting occurs, the frozen ground resists seepage of liquid water. Consequently, the embedded moisture probes sense very little water in soil during winter. In addition, compared with precipitation, the change of daily soil moisture has a delayed response. To better understand the soil moisture temporal variation, the standard deviation (Std) and the coefficient of variations (CV) of soil moisture data are determined (Fig. 2b and c).

CV j ¼

ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 1 ðh  h Þ ij i i¼1 N hj

ð1Þ

hi ¼

M 1X hij M j¼1

ð2Þ

hj ¼

N 1X hij N i¼1

ð3Þ

where N is the sum of sites; M is observation times over a period; hij means the soil moisture of site i at time j. In this study, N = 15 at 5 cm depth (10 cm, N = 14); M = 428; The standard deviation reflects the degree of dispersion, and the CV, a normalized variable of the dispersion degree, is better suited to describe the discrete variation of a time series, which can be attributed to its non-dimensional trait. Analysis of the variation of Std and CV at 5 and 10 cm depths can reveal some interesting results. For example, overall variation of these indices are similar

in two measured layers, and reveals seasonal cycles in daily soil moisture content. CV in particular exhibits significant fluctuations with seasonal transition, especially during the freezing and thawing seasons. However, Std is stable. Daily soil moisture has a larger value than Std and CV in wetter summer, which means soil moisture is a stable time series and has a low degree of dispersion. Winter is just the opposite. Daily soil moisture values are low, but Std and CV are increasing. It shows a high dispersion degree in winter and exhibits a significant difference from the annual mean soil moisture. 3. Methodology The methods used in this study can be divided into four categories. Random sampling–NRS analysis balance between the representativeness and the economic cost. Time stability analysis (TSA) and time sliding correlation analysis (TSCA) provide a representative sampling site that reflects the regional soil moisture changes. Optimal combination of sites (OCS) extracts the best matching sites, and a range of commonly used up-scaling methods, such as average relative deviation substitution (ARDS), absolute deviation analysis (ADA), linear fit, and cumulative distribution function matching (CDFM), are studied to get the soil moisture in regional scale. Details of these methods are shown in next sections. 3.1. Random sampling–NRS analysis In a given research area, Std and CV of soil moisture will increase with the spatial scale (Crow et al., 2012) and establishment of a large sample space is an effective way of solving this problem (De Rosnay et al., 2009). Regional soil moisture estimation will be more precise if more sites are contained in a specific sampling area, but the cost for installing and maintaining the observation network will increase. It is necessary to balance the cost and the precision of regional soil moisture estimation with the goal of obtaining more soil moisture information with fewer sites,

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

65

Fig. 2. The temporal variations of mean soil moisture, Std and CV in Maqu SM-network from July 1, 2011 to August 31, 2012. (a) The mean soil moisture and ECMWF daily rainfall. (b and c) The Std and CV of soil moisture at 5 and 10 cm depths (unit: m3/m3).

namely, producing greater profits with less cost. NRS analyses can help confirm the specific number and serial number of the sampling sites (Hills and Reynolds, 1969). NRS is acquired through random sampling analysis in this study with the advantage of not requiring assumptions in the sampling statistical distribution. Wang et al. (2008) has implemented NRS analysis on different scales with different confidence levels and relative errors. Root mean square difference (RMSD) and correlation coefficient (R) are defined as follows:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PM 2 0 j¼1 ðhj  hj Þ RMSDn ¼ M

ð4Þ

Rn ¼

cov ðhj 0 ; hj Þ stdðhj 0 Þ  stdðhj Þ

ð5Þ

hj 0 ¼

n 1X hij n i¼1

ð6Þ

where N is the sum of sites; n is number of sampled sites in one subset; M is observation times over a period; hij means the soil moisture of site i at time j. The maximum number of subsets in each sampling loop was set as 10,000, mmax = 10,000, to obtain a consensus with ergodicity in mathematics. Construction of the random sampling approach is as follows:

66

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

Step 1: Prepare sampling population, set n = 1, m = 1. Here n is the number of sampled sites within a subset and m denotes the mth sampled subset (mmax = 10,000). Step 2: Randomly select n sites from population into the mth subset. Calculate RMSDn,m and Rn,m. Step 3: Set m = m + 1, repeat Step2 until m = mmax. Calculate the mean value of RMSD and R, namely RMSDn and Rn , and standard deviation std(RMSD)n and std(R)n. Step 4: Set n = n + 1, repeat Step2–Step4 until n = N. RMSDn decreases with the increasing of n, meanwhile, Rn also will increase; when n = N, RMSDN ¼ 0, RN ¼ 1, so the minimum n under a certain accuracy requirement of RMSD and R can be ascertained. n is what we called NRS. 3.2. Time stability analysis (TSA) For a relatively small spatial area, the most representative single site might exists, because sites are highly correlated (Brocca et al., 2009). Independent studies have found one representative site is able to estimate the actual soil moisture variation in regional scale. Brocca and Martínez-Fernández demonstrated this on 200 km2 and 1000 km2 scales (Brocca et al., 2012; MartínezFernández and Ceballos, 2005). TSA is based on the relative difference analysis which Vachaud first used in searching for the representative sites (Vachaud et al., 1985). In theory, it is impossible to obtain the ‘‘ground truth” of regional soil moisture. Here the mean value of total sites is regarded as ‘‘the true value”, so the relative difference of soil moisture can be expressed as follows:

dij ¼

hij  hj hj

ð7Þ

where i is the serial number of sites (i = 1, 2, 3, . . . N); j is the number of observations (j = 1, 2, 3 . . . M); hj is the spatial mean at time j; dij is the relative difference of site i at time j to measure the deviation of a single site compared with ‘‘the true value”. Through the whole time series, the mean relative difference and standard deviation of relative difference are used.

di ¼

ri

M 1X dij M j¼1

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 XM  ¼ dij  di j¼1 M1

1 X hik 15 k¼j

ð12Þ

Pj ¼

1 X hk 15 k¼j

ð13Þ

jþ14

jþ14

where M is observation times over a period; hij means the soil moisture of site i at time j; ri,j is time sliding correlation coefficient with a step of 15 days. TSA and TSCA can obtain representative single sites at each depth. Although a single site may contain the main soil moisture information in this area, and thereby has the best value compared with others, it is obvious that a large amount of useful details are lost. Therefore, it is a risk to estimate regional soil moisture from a single site. Zhao proposed OCS to calculate the regional value (Zhao et al., 2013). That is, using the random sampling approach to obtain a set of sites with high-quality, which contain more effective information of soil moisture and its average is what we desired as ‘‘single site”. This method could balance the high economic costs (equipment, employee time, and maintenance) of field work with the risk of less reliable data when using a smaller set of representative samples. The specific operation is the same as the method mentioned in Section 3.1, and selecting the first three as combination sites. 3.4. Up-scaling methods TSA, TSCA, and OCS provide us a single representative site, which is treated as a reference for further research. Considerable differences between the single representative site and the ‘‘ground truth” still exist and this gap can be filled by some statistical methods to obtain a better regional soil moisture series. Up-scaling methods transform single site data, uij = hij, to regional soil moisture, yb ¼ hb , which can be used to validate the results obtained j

j

by satellite retrieval. Some commonly used up-scaling algorithms will be introduced later and the purpose of this narrative is search for the optimum up-scaling method that suitable for the Maqu region. Four algorithms are shown as follows.

ð8Þ (1) Average relative deviation substitution (ARDS)

ð9Þ

where di and ri are the mean relative difference and standard deviation of relative difference of site i respectively. Jacobs considered these two factors and presented a comprehensive evaluation criterion g (Jacobs et al., 2004).

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gi ¼ di 2 þ r2i

Lij ¼

ð10Þ

ybj ¼

uij di þ 1

ð14Þ

This expression is the transformation of Eq. (5) with dij replaced by its time average, di . Nevertheless, di does not provide an unbiased estimator in the case of noise on the hj signal and differences from the spatially averaged soil moisture have a low weight in di , in case the spatial averaged soil moisture is high. (2) Absolute deviation analysis (ADA)

Site i is representative if gi is small enough.

a ybj ¼ uij  hdj i

3.3. TSCA and OCS

ð15Þ

a

where hdj i ¼ meanðuij  hj Þ. To some extent, looking for the most representative site strikes a balance in the correlation degree between the ‘‘ground truth” and single site value. What we concerned is a site that can describe the regional variations on a year-scale, so it is better to use the time sliding correlation analyses, because it can crowd in all data in a year, including the extensive changing caused by the freezing– thawing process.

PM

j¼1 ðhij

 Lij Þðhj  Pj Þ r i;j ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PM 2 2 PN j¼1 ðhij  Lij Þ j¼1 ðhj  P j Þ

ð11Þ

(3) Linear fitting

ybj ¼ a þ b  uij

ð16Þ

where a and b are constant parameters. (4) Cumulative distribution function matching (CDFM) With respect to probability distribution, the values of soil moisture in a year has its probability of occurrence, in other words, the probability density function can be derived. However, matching

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

result for a discrete probability density function is not as good as desired, because the change of soil moisture is successive in time domain, but the total values are impossible to be recorded. Cumulative distribution function (CDF) obeys the value range from 0 to 1 and it favors limiting the estimation error. CDFM provides a fresh idea to get the regional soil moisture by bridging the distribution of a single site and the sites average (black arrow line shown in Fig. 3) through CDF. This method has been used in many research fields (Drusch et al., 2005; Reichle and Koster, 2004). Fig. 3 shows cumulative distribution function matching between the representative site obtained by time stability analyses at 5 cm depth and the average time series. The first step is arranging values in an ascending order, and then determining the value of f(x), where f is a CDF. Second and third order polynomials are applied respectively. 4. Results and discussion 4.1. NRS analyses NRS and specific sites can be found under a given value of RMSD and R, which serve as a criterion. Fig. 4 shows the variation tendency of RMSD and R with the increase in number of sampling sites. This describes the degree of dispersion, but demonstrates a negative correlation. At the beginning, a large RMSD (or low R) is obtained with a small number of sampling sites, while its value decreases (or increases) rapidly as the number of sites increases. Both RMSD and R change slightly and approach relatively stable values as the number of sites increased. This is reasonable, because a large number of samples yield a more precise estimation. For measuring uncertainties in Maqu SM-network, a compromised criterion of R P 0:99; RMSD 6 0:02 m3 =m3 was used (Zhao et al., 2013). Table 1 shows NRS and specific sites at 5 and 10 cm depths. We find that NRS = 10 in both layers, but the specific sites are not exactly the same. It is crucial to determine the depth research emphasized and then formulate the network according to NRS. NRS will vary from spatial scales, accuracy levels and the total deployed sites. Research shows that NRS will range between 4 and 15 in the field, and increase to 40 at the catchment scale under an absolute error criterion of 0.02 m3/m3 (Brocca et al., 2009). The research on NRS is necessary to provide an important reference for planning and establishing an observation network. 4.2. TSA Determination of representative soil moisture single sites has been discussed using the theory of time stability at 5 cm (15 sites)

67

and 10 cm (14 sites) depths. All sites are sorted in an ascending order according to the value of mean relative difference, as shown in Fig. 5, and the vertical bar is standard deviation of the relative difference. The time averaged relative difference, di , and temporal standard deviation, ri, can be used as criteria to balance the spatial representativeness. A representative site can be justified as one for which di is close to 0.0, or has a small ri, which means this site shows a similar temporal evolution in soil moisture as the spatial average. A site with this characteristic is time-stable. Generally, sites have relatively low ri in arid regions, where di has a negative value (Jacobs et al., 2004). In terms of the averaged relative difference, the minimum value at 5 cm (10 cm) depth is 0.018 (0.023), corresponding to site NST13 (CST03). On the side of standard deviation of relative difference, the minimum site is NST01 (0.058) and CST05 (0.065) in the two layers, respectively. This analysis shows that a representative single site is upon criterion and sampling depths. Although the results are different for the two criterions, they have a positive correlation, which is why the method mentioned by Jacobs can be used to make a comprehensive analysis, the blue line shown in Fig. 5 is index gi. The most attractive representative site would be one whose di and ri are close to 0. The minimum of gi for 5 cm (10 cm) is 0.068 (0.088) and the homologous site is NST01 (NST07). Consequently, NST01 and NST07 are representative sites in 5 and 10 cm depth as determined from the time stability analysis. RMSD between the time series of point measurements and spatial mean value is minimal, i.e., 0.032 m3/m3 and 0.029 m3/m3. Different depths have different representative sites, which might be attributed to the significant intricate hydrological processes. Soil layer is a very intricate system. Its texture, porosity and underground water table, will make different effects on hydrologic variability in each layer. In addition, upper layers, where have great response to climate change, vegetation, uneven distribution of terrain, precipitation, and runoff, are more complicated and changeable, and that is what the further study need to concern.

4.3. TSCA Pearson correlation is a statistic method used for measuring the degree of correlation of two variables. TSCA uses the data in a fixed time range, namely a time step, so as to exclude outside disturbances and improve the accuracy of correlation. Time step in this study is 15 days. Time sliding correlations coefficient between each site and spatial mean values in two layers are depicted in Fig. 6 where the red line denotes the maximum TSCA correlation. Using

Fig. 3. The CDFM of NST01 in Maqu SM-network (unit: m3/m3).

68

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

Fig. 4. The variation of RMSD and R at 5 cm and 10 cm depths with the number of sampled sites at daily scale in Maqu SM-network (unit: m3/m3).

Table 1 The NRS and specific sites of Maqu SM-network at 5 cm and 10 cm depths. Observation depth (cm)

NRS

Sites

R/RMSD (m3/m3)

5

10

10

10

CST03 CST04 NST01 NST02 NST07 NST08 NST11 NST12 NST13 NST14 CST03 CST04 CST05 NST01 NST03 NST06 NST07 NST09 NST11 NST14

0.9971/ 0.0181 0. 9937/ 0.0184

this analysis, NST01 and NST02 are representative sites in 5 and 10 cm depths, and the correlation coefficients are 0.930 and 0.892, respectively. The results of the time stability analysis and time sliding correlation analysis are consistent at 5 cm depth, but inconsistent at 10 cm. A representative single site roughly describes the variation of regional soil moisture and further study has implemented it in the data up-scaling. Consequently, the difference at 10 cm is not crucial, and it is important to judge the representative site after up-scaling, using RMSD as the criterion. 4.4. OCS analysis

subjective. Based on the former investigation (Zhao et al., 2013), three sites are to be chosen for evaluation and validation in our study. Table 2 lists the top 5 combinations with the smallest value of RMSD. OCS at 5 cm are NST01, NST03, and NST07 which have the smallest RMSD = 0.015 m3/m3 and the sites at 10 cm depth are NST05, NST08, and NST13 with RMSD = 0.017 m3/m3. That the value of RMSD at 5 cm depth is smaller might be attributed to its larger number of sites in this layer. A high correlation is found between OCS and the results of time stability analysis and time sliding correlation. OCS at 5 cm depth contains NST01, and this site possessed a high proportion in top-ranking combinations. Likewise, NST07 and NST02 at 10 cm depth. 4.5. Up-scaling analyses Different up-scaling algorithms are used to obtain the spatial representativeness of a single site. Fig. 7(a) and (b) are the same, because TSA and TSCA have a common result at 5 cm depth. The figure shows that linear fitting is the best method for it has the minimum value, RMSD = 0.019 m3/m3. The relationship is expressed as follows.

SMregion ¼ 1:1045  SMsingle OCS, which based on the random sampling analysis, was used to choose the optimal combination of sites and then serve their average time series as the value of representative ‘‘single site”. Zhao used a sensitivity study on a number of combined sites, and showed that the number of combinations, which have specified number of sites, increasing under a lower RMSD criterion. In other words, the number will become larger if the sites in one combination are increasing under the specified RMSD criterion (Zhao et al., 2013). It means the selection of the number of combined sites is

þ 0:0178 ðTSA and TSCA at 5 cm depthÞ

ð17Þ

During the wet season, ADA and ADRS take second place and CDFM is even worse than a purely single site estimate. In dry winter, linear fitting is the only method for moisture estimation. CDFM hardly describe the estimation in annual scale, especially in winter when presents the maximum difference in two layers, because the largest and exhaustive statistic information all the year around are used in each time, while great distinction exists between the

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

Fig. 5. Rank order mean relative difference with its standard deviation (vertical bar) and g for different depth.

Fig. 6. TSCA of different sites in two layers in Maqu SM-network.

69

70

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

Table 2 The results of OCS analysis at 5 cm and 10 cm depths. N1

N2

N3

RMSD (m3/m3)

5

NST01 NST03 NST01 NST03 NST03

NST03 NST12 NST07 NST06 NST06

NST07 NST14 NST14 NST13 NST14

0.015 0.017 0.017 0.017 0.017

10

NST05 NST05 NST02 NST05 NST02

NST08 NST07 NST03 NST06 NST05

NST13 NST08 NST08 NST13 NST08

0.017 0.018 0.019 0.020 0.020

Observation depth (cm)

freezing and thawing reasons; Both ARDS and ADA take mean vala ues, di or hdj i, replace the instantaneous values, which also can be attributed to freeze–thaw, but the difference is smaller than CDFM for mean value they used in each time is equal. Linear fitting is a method keeps the characteristics in each stage well, in fact, its equation is in close proximity to the equations obtained in freezing and thawing periods, respectively. Freezing and thawing periods should be investigated separately in the further study. The representative site under TSA and TSCA at 10 cm depth are NST07 and NST02 respectively, and the scale up results are shown in Fig. 7 (d) and (e). The Linear fitting is still the optimum method due to its small RMSD (0.024 m3/m3 and 0.012 m3/m3). The up-scaling equations are:

Fig. 7. The results of representative single site up-scaled in Maqu SM-network at 5 cm and 10 cm depths. (a) TSA-single site at 5 cm depth. (b) TSCA-single site at 5 cm depth. (c) OCS-single site at 5 cm depth. (d) TSA-single site at 10 cm depth. (e) TSCA-single site at 10 cm depth. (f) OCS-single site at 10 cm depth (unit: m3/m3).

71

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

Fig. 7 (continued)

SMregion ¼ 0:08567  SMsingle þ 0:05593 ðTSA at 10 cm depthÞ

SMregion ¼ 0:9799  SMsingle þ 0:00293 ðOCS at 5 cm depthÞ

ð18Þ

ð20Þ and

SMregion ¼ 0:7022  SMsingle þ 0:883 ðTSCA at 10 cm depthÞ ð19Þ Other methods are poor at depicting regional variation trends especially in winter, and little individual data will achieve positive effects after scale up in wet periods. Because OCS has larger formation content of soil moisture, it is reasonable that it will yield better up-scaling result, which is clearly shown in Fig. 7(c) and (f). Estimations are much closer to the ‘‘ground truth” owing to the tremendous contributions of up-scaling methods at 5 and 10 cm depths. These methods are able to satisfy different accuracy requirements, but linear fitting is still the best of all. Linear fitting equations at two depths are:

SMregion ¼ 1:0115  SMsingle þ 0:0059 ðOCS at 10 cm depthÞ ð21Þ 3

3

3

3

with RMSD = 0.014 m /m and 0.014 m /m , which is higher than TSA and TSCA. In conclusion, to obtain the regional soil moisture content, it is sensible to use linear fitting based on OCS ‘‘single site” data if three optimum combination sites are integrated, or the single sites of TSA and TSCA used in substitution. Much data from Maqu SM-network during 2013–2014 is lost, only 10 sites are well preserved (about 50%), thus, it is unreliable to use the average value of these sites as ‘‘the true value” in this region (black line shown in Fig. 8). However, the established linear fitting equations can offer a

72

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

Fig. 8. The estimated regional soil moisture in Maqu SM-network during 2013 and 2014. (a) The estimated value by using TSA, TSCA and OCS at 5 cm depth, (b) the estimated value by using TSCA at 10 cm depth (unit: m3/m3).

more accurate estimation. At 5 cm depth, Eq. (15) is used to upscaling the ‘‘single site” data for OCS, NST01, NST03, and NST07, are existing (shown as Fig. 8(a)). At 10 cm depth, Eq. (14) is used as optimal data up-scaling transformation, because the combination sites in OCS and representative single site in TSA are incomplete. 5. Summary and conclusions Employing on the site-observed soil moisture data in Maqu SM-network during July 1, 2011 to August 31, 2012 at 5 and 10 cm depths, NRS analysis, representative single site analysis, and up-scaling methods analysis are conducted in this study. The results produced the following conclusions: (1) In Maqu SM-network, generally an NRS = 13 is obtained under the criterion of R P 0.99, RMSD 6 0.02 m3/m3 at both 5 and 10 cm sampling depths. The specific sites for these analyses are CST03, CST04, NST01, NST02, NST07, NST08, NST11, NST12, NST13, and NST14 at 5 cm depth and CST03, CST04, CST05, NST01, NST03, NST06, NST07, NST09, NST11, NST14 at 10 cm depth. It is crucial to determine the depth that research emphasized first, and then formulate the network based on the specific NRS. (2) Index gi in time stability analysis is a comprehensive variable compared with time averaged relative difference and temporal standard deviation. The representative single sites in two sampling depths are NST01 and NST07, respectively. NST01 and NST02 are representative sites under time sliding correlation analysis. OCS contains more effective information of soil moisture, and the representativeness of the ‘‘single site” must be superior to other methods. The optimum

combinations of the sites for two sampling layers are NST01, NST03, NST07 and NST05, NST08, NST13, respectively. (3) Four commonly used up-scaling methods, including average relative deviation substitution, absolute deviation analysis, linear fit, and cumulative distribution function matching, are deployed to enhance the spatial representativeness of single site. The results shows that linear fitting is the best up-scaling method for all types of the representative single sites in two layers. OCS has the greatest effect, time sliding correlation takes the second place. In this investigation, the average value of sampling sites are taken as the ‘‘ground truth” of this region and be used to conduct the NRS analysis, representative single site analysis, and establish optimum linear fitting equations. There are considerable differences between the average value and ‘‘ground truth” owing to non-homogeneous underlying surface and vegetation. Further studies should concentrate on acquiring the ‘‘ground truth”. This is potential to test a different texture and make an intercomparison, and it is to be considered in further investigation. In addition, the freeze–thaw process of soil has a huge impact on up-scaling methods, so freeze and thaw periods should be considered separately.

Acknowledgements This study was supported by funding from the National Natural Science Foundation of China (Grant Nos. 41375022 and 41530529) and the Key Research Program of the Chinese Academy of Sciences

J. Chen et al. / Journal of Hydrology 533 (2016) 62–73

(Grant KZZD-EW-13). The authors are grateful to the anonymous reviewers for their constructive comments. References Bian, L., Gao, Z., Ma, Y., Koike, T., Ma, Y., Li, Y., 2012. Seasonal variation in turbulent fluxes over tibetan plateau and its surrounding areas: research note. J. Meteorol. Soc. Jpn 90C, 157–171. Brocca, L., Melone, F., Moramarco, T., Morbidelli, R., 2009. Soil moisture temporal stability over experimental areas in Central Italy. Geoderma 148 (3–4), 364– 374. Brocca, L., Tullo, T., Melone, F., Moramarco, T., Morbidelli, R., 2012. Catchment scale soil moisture spatial–temporal variability. J. Hydrol. 422–423, 63–75. Crow, W.T., Ryu, D., Famiglietti, J.S., 2005. Upscaling of field-scale soil moisture measurements using distributed land surface modeling. Adv. Water Resour. 28 (1), 1–14. Crow, W.T. et al., 2012. Upscaling sparse ground-based soil moisture observations for the validation of coarse-resolution satellite soil moisture products. Rev. Geophys. 50 (2), RG2002. Drusch, M., Wood, E.F., Gao, H., 2005. Observation operators for the direct assimilation of TRMM microwave imager retrieved soil moisture. Geophys. Res. Lett. 32 (15), L15403. Dente, L., Vekerdy, Z., Wen, J., Su, Z., 2012. Maqu network for validation of satellitederived soil moisture products. Int. J. Appl. Earth Obs. Geoinf. 17, 55–65. De Lannoy, G.J.M., Houser, P.R., Verhoest, N.E.C., Pauwels, V.R.N., Gish, T.J., 2007. Upscaling of point soil moisture measurements to field averages at the OPE3 test site. J. Hydrol. 343 (1–2), 1–11. De Rosnay, P., Gruhier, C., Timouk, F., Baup, F., Mougin, E., Hiernaux, P., et al., 2009. Multi-scale soil moisture measurements at the Gourma meso-scale site in Mali. J. Hydrol. 375 (1–2), 241–252. Entekhabi, D. et al., 2010. The soil moisture active passive (SMAP) mission. Proc. IEEE 98, 704–716. Guo, M., 2009. Research of Vegetation Coverage Distribution Changes of Alpine Grassland Based on 3s Technology (Master). Lanzhou University. Hills, R.C., Reynolds, S.G., 1969. Illustrations of soil moisture variability in selected areas and plots of different sizes. J. Hydrol. 8 (1), 27–47. Hong, S.Y., Pan, H.L., 2000. Impact of soil moisture anomalies on seasonal, summertime circulation over North America in a regional climate model. J. Geophys. Res. – Atmos. 105 (D24), 29625–29634. Jung, M., Reichstein, M., Ciais, P., Seneviratne, S.I., Sheffield, J., Goulden, M.L., et al., 2010. Recent decline in the global land evapotranspiration trend due to limited moisture supply. Nature 467 (7318), 951–954. Jacobs, J.M., Mohanty, B.P., Hsu, E.C., Miller, D., 2004. SMEX02: field scale variability, time stability and similarity of soil moisture. Remote Sens. Environ. 92 (4), 436–446. Kerr, Y.H., Waldteufel, P., Wigneron, J.P., Martinuzzi, J.M., Font, J., Berger, M., 2001. Soil moisture retrieval from space: the soil moisture and ocean salinity (SMOS) mission. IEEE Trans. Geosci. Remote Sens. 39 (8), 1729–1735.

73

Liu, S., Sun, R., Sun, Z., Li, X., Liu, C., 2004. Comparison of different complementary relationship modes for regional evapotranspiration estimation. Acta Geogr. Sin. 03, 331–340. Ma, Z., Fu, C., Li, X., Chen, W., Tao, S., 2001. Some problems in the study on the relationship between soil moisture and climate change. Adv. Earth Sci. 04, 563– 568. Martínez-Fernández, J., Ceballos, A., 2005. Mean soil moisture estimation using temporal stability analysis. J. Hydrol. 312 (1–4), 28–38. Reichle, R.H., Koster, R.D., 2004. Bias reduction in short records of satellite soil moisture. Geophys. Res. Lett. 31 (19), L19501. Robock, A., Vinnikov, K.Y., Srinivasan, G., Entin, J.K., Hollinger, S.E., Speranskaya, N. A., et al., 2000. The global soil moisture data bank. Bull. Am. Meteorol. Soc. 81 (6), 1281–1299. Sun, R., Liu, C., Zhu, Q., 2001. Relationship between the fractional vegetation cover change and rainfall in the Yellow River basin. Acta Geogr. Sin. 06, 667–672. Shi, J., Jiang, L., Zhang, L., Chen, K.S., Wigneron, J.-P., Chanzy, A., et al., 2006. Physically based estimation of bare-surface soil moisture with the passive radiometers. IEEE Trans. Geosci. Remote Sens. 44 (11), 3145–3153. Tian, H., Wen, J., Shi, X., Wang, X., Liu, R., Zhang, J., Lv, S., 2011. Estimation of soil moisture in summer by active microwave remote sensing for the Maqu area at the upper reaches of the Yellow River. Adv. Water Sci. 01, 59–66. Vachaud, G., Desilans, A.P., Balabanis, P., Vauclin, M., 1985. Temporal stability of spatially measured soil–water probability density-function. Soil Sci. Soc. Am. J. 49 (4), 822–828. Vinnikov, K.Y., Robock, A., Qiu, S., Entin, J.K., 1999. Optimal design of surface networks for observation of soil moisture. J. Geophys. Res. – Atmos. 104 (D16), 19743–19749. Wang, L., Wen, J., Wei, Z., Hu, Z., Zhao, Y., Wei, R., 2008. Soil moisture on the west of northwest China and its response to climate. Plateau Meteorol. 06, 1257–1266. Wei, Z., Dong, W., Hui, X., 2000. Evolution of trend and interannual oscillatory variabilities of precipitation over northwest China. Acta Meteorol. Sin. 02, 234–243. Wen, J., Jackson, T.J., Bindlish, R., Hsu, A.Y., Su, Z., 2005. Retrieval of soil moisture and vegetation water content using SSM/I data over a corn and soybean region. J. Hydrometeorol. 6 (6), 854–863. Wen, J., Su, Z., Ma, Y., 2003. Determination of land surface temperature and soil moisture from tropical rainfall measuring mission/microwave imager remote sensing data. J. Geophys. Res. – Atmos. 108 (D2), 1–10. Yang, K., Qin, J., Zhao, L., Chen, Y., Tang, W., Han, M., et al., 2013. A multiscale soil moisture and freeze–thaw monitoring network on the third pole. Bull. Am. Meteorol. Soc. 94 (12), 1907–1916. Zhang, L., Zhang, Y., Zhang, X., Wu, B., 2004. A short-term model of grain supply– demand balance based on remote sensing for crop monitoring and agriculture statistical data. J. Remote Sens. 06, 645–654. Zhao, L., Yang, K., Qin, J., Chen, Y., Tang, W., Montzka, C., et al., 2013. Spatiotemporal analysis of soil moisture observations within a Tibetan mesoscale area and its implication to regional soil moisture measurements. J. Hydrol. 482, 92–104.