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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This study evaluates if the temporal stability concept is applicable to a time series of satellite soil moisture images so to extend the common procedure of satellite image validation. The area of study is the Maqu area, which is located in the northeastern part of the Tibetan plateau. The network serves validation purposes of coarse scale (25–50 km) satellite soil moisture products and comprises 20 stations with probes installed at depths of 5, 10, 20, 40, 80 cm. The study period is 2009. The temporal stability concept is applied to all five depths of the soil moisture measuring network and to a time series of satellite-based moisture products from the Advance Microwave Scanning Radiometer (AMSR-E). The

Soil moisture is a fundamentally important variable in the hydrological and energy cycle. In the hydrological cycle, moisture influences processes such as infiltration, recharge, but also generation of runoff processes such as interflow and overland flow [^{2}), satellite observations are at the pixel footprint scale that, for instance, may be as large as 25 km × 25 km for AMSR-E or 50 km × 50 km for the SMOS satellite mission. Moreover, satellite observations provide information for shallow (<5 cm) land surface depths due to limited penetration [

Validation is imperative in order to make any conclusions about the reliability of satellite observations [

In satellite validation, it is common to compare satellite observations to field (

Validation of satellite observations commonly relies on: (i) scatter plots where field measured moisture is plotted against satellite-based soil moisture to indicate how well values match [

Challenging to validation is: (i) to understand the content of the information that is embedded in the ^{2} is shown in Dente

A second method to assess characteristics of temporal stability is correlation analysis [

This paper is organized as follows: in Section 2, the study area and data are presented. The applied methodology is described in Section 3, which is divided in three sub-sections: the temporal stability concept, correlation analysis and time series analysis. Hereafter, in Section 4 the results are described and discussed and in Section 5 conclusions are drawn.

For this study, the Maqu area is selected. It is situated in the northeastern part of the Tibetan Plateau and located southeast of Maqu city, on the border between Gansu and Sichuan provinces, China (33°30′–34°15′ N latitude, 101°38′–102°45′ E longitude). The area has an elevation ranging from 3,160–4,664 m.a.s.l. and is characterized by the river valleys of the Yellow River, the Black River and the Lang River mountain ranges towards the area divide. Topographically, the Maqu area is characterized by hills, valleys, rivers, wetlands, grassland and bare areas with uniform land cover of short grassland and some wetlands. Soil texture mostly is silt loam with organic matter that is higher in wetland areas than in grassland areas. According to the Köppen Classification System [

In the Maqu area, a soil moisture and soil temperature monitoring network of 20 stations has been installed by Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences (CAREERI, CAS) and ITC (Faculty of Geo-Information Science and Earth Observation, University of Twente, Enschede, The Netherlands). Stations record and store data at 15 min interval, which serve for validation of SMOS, ASCAT and AMSR-E satellite missions.

The network covers an area of approximately 80 km × 40 km. Station locations have been selected to monitor the area at different altitudes and slopes with variable land cover and soil type [

During the installation of the stations, soil samples were collected to analyze bulk density, particle size distribution and organic matter content. Most of the stations are installed in silt loam soils, except for stations N9 and N10 that are characterized by sandy loam and loam-silt soils, respectively. The wetland stations N4 and N11 have the highest organic matter content (>130 g/kg), all the other stations are installed in areas with low organic content (<60 g/kg).

For each station, a number of soil moisture and soil temperature probes are installed. Stations C1-5, N1, N12 have measuring probes at 5, 10, 20, 40 and 80 cm depth, stations N5, N6, N10, N13 have probes till 40 cm depth whereas stations N2, N3, N4, N7, N8, N9, N11, N14, N15 collect data only at 5 and 10 cm depth.

Each station is equipped with an Em50 ECH20 data logger that records the soil moisture data at 15 min interval of the ECH2O EC-TM probes. As part of the installation of the network, recorded soil moisture data has been compared and calibrated against volumetric soil moisture measurements obtained by gravimetric sampling at all station locations. After calibration, the root mean square difference was found to be 0.02 m^{3}·m^{−3}[

All soil moisture time series are screened for moisture values higher than the porosity value (0.55) of the shallow silt loam soil layer in the Maqu area. Time series from five stations (C2 at 80 cm, N4 at 5 and 10 cm, N5 at 5 cm and N15 at 5 cm) were excluded from further use since measurements systematically indicated moisture contents much higher than the maximum possible (

For this study, we use daily time series of the soil moisture products from the AQUA AMSR-E sensor as post-processed by the Vrije Universiteit Amsterdam (VUA) in The Netherlands and the National Aeronautics and Space Administration (NASA), in the USA [

Time series of all pixels are screened for values higher than the porosity value of the shallow soil layer. Results of screening indicated that time series of pixels P1, P2, P5, P6, P7, P11 are unreliable. We noticed that all these pixels overlay hilly terrain and signals that time series of the remaining (few) pixels that overlay hilly terrain may be doubtful as well. As such for application of the temporal stability concept, we also excluded time series of pixels P3, P4 and P12 and only used time series of pixels P8, P9, P10, P13, P14 and P15 that overlay flat terrain.

For assessing and comparing statistics of the time series of the network stations, a MRD plot [_{i}_{ij}_{ij}_{j}

MRD plots are prepared for each of the five probe depths and for time series of AMSR-E VUA satellite images. For the latter, daily images are ordered chronologically and the MRD value is calculated for each pixel. The satellite-based MRD plot identifies the pixel that indicates the area RMSM. The station based MRD plots at four probe depths (5, 10, 20 and 40 cm) are evaluated for persistence to serve for satellite validation.

Following Cosh _{j,j}_{′}) to assess correlation of moisture patterns over time:
_{i}_{j}_{i}_{j}_{′} are soil moisture observations for station i for given time instants _{·,}_{j}

A second application of Pearson's correlation coefficient (_{i}_{i}_{′}) is shown in Cosh _{i}_{j}_{i}_{′},_{j}_{i,i}_{′} range between +1 and −1 with uncorrelated stations having _{i}_{i}_{′} value close to 0. In Cosh _{i}_{i}_{′}| > 0.7 which indicates stable moisture patterns by the network. Low correlation is suggested when |_{i}_{i}_{′}| > 0.3 which indicates that moisture patterns differ in the network. In this study, we adopted these value ranges.

We inter-compared station and satellite data for identification of periods with large and/or small deviations. We calculated the RMSE and Bias (

MRD plots for respective moisture probe depths (

For RMSM station N1 at 5 cm depth, the station indicates dry and wet conditions for 40 and 80 cm respectively but close to RMSM conditions for 10 and 20 cm depth. The RMSM station N2 at 10 cm depth shows a relatively dry condition for 5 cm depth but observations for other depths are not available. RMSM station C2 at 20 cm indicates MSM close to RMSM for depth 5 cm, 10 cm and 40 cm. As such, identification of a RMSM station for certain probe depth not necessarily implies that such station indicates the RMSM over the area.

Inter-comparison of MRD plots from 5 cm depth to 80 cm depth shows that the range of box values becomes smaller and closer to the box value of the RMSM station (^{3}·m^{−3} for the RMSM station at 5, 10, 20, 40 and 80 cm depth, respectively. It indicates that on annual basis, soils at depths of 40 and 80 cm are dryer than soils at shallower depth. It suggests that much infiltration water is stored at shallow depths (5–20 cm), thus causing the relative large differences in MRD across the network stations at 5 cm and 10 cm in particular.

To evaluate the relationship between daily average soil moisture of the RMSM station and the corresponding daily MSM of the remaining stations of the network, a scatter plot (^{2}) ranges between 0.69–0.92. R^{2} values higher than 0.75 are indicated at 5, 10, 40 and 80 cm depth. We note that R^{2} values compare well to values reported in [^{2} value (0.69) is found at 20 cm depth, which is caused by overestimation of MSM by the selected RMSM station at this depth (see ^{2} values suggest that variability of area MSM at respective probe depths can be represented by the selected RMSM station.

Pearson correlation plot in

Pearson's correlation plots (

To further evaluate temporal persistence, we assessed occurrence in % of the high, medium or low correlation classes (

Bar graphs show relatively high occurrence of the high correlation class for both the network and the RMSM station at all probe depths. The average occurrence for high correlation over all depths was found to be 61% and 64% for the RMSM station and network average stations respectively. It suggests that the patterns of both the network average and the RMSM station are persistent over time. To further assess how well temporal patterns are represented by the RMSM station, we inter-compared occurrence at respective depths. Results at 5 cm show largest deviation between the network and the RMSM station with lowest occurrence of high correlation observed among all depths. At 10 cm depth, high % of occurrence (68% and 66%) of the high correlation class was found for both the network and the RMSM station respectively. It indicates that the RMSM station and network equally well represents temporal persistence. A higher value for both occurrences is only observed at 40 cm for the RMSM station, which by itself is not surprising given the outcomes of the temporal stability concept. Overall, it suggests that the selected RMSM station at 10 cm depth best represents the temporal persistence as compared to the RMSM stations at other probe depths.

After selecting the RMSM station, the temporal stability analysis (Equations (

The MRD plot shows that pixel P15 has MRD value −1.3% that is closest to zero with SD(MRD) of 5.8%. Following the principles of the temporal stability concept, we identify this pixel as the RMSM pixel that should indicate the satellite-based RMSM. The MRD plot in

MRD plots (

To further evaluate how well network observations are represented by satellite images, we compared daily time series from the network to four series that are from the RMSM station, the RMSM pixel, the average of the image pixels and the pixel that overlays the RMSM station (

Visual inspection of the moisture time series of the network average and the RMSM station at 5 cm shows a good match in general except in July where the network indicates higher values. Both time series, however, show lower moisture compared to time series of the satellite-based RMSM pixel and the average of the image pixels. Further, satellite-based time series show much lower temporal variability compared to the network average and the RMSM station observations. Time series of the overlay pixel show values that largely deviate from the RMSM station, the RMSM pixel and the average of the image pixels. Further, the overlay pixel shows higher moisture values and indicates higher variability. We note that both RMSE and Bias have similar value for the RMSM pixel, the average of the image pixels and the overlay pixel.

Visual inspection of the time series at 10 cm depth shows several periods where the RMSM station observation deviates from the network observation. Similar to the comparison at 5 cm, the RMSM station underestimates the network average for the month of July, but for the period August–November, overestimation is indicated. For this period, however, a fair match is shown for the RMSM station and all three satellite-based time series. At deeper depth (20 cm and 40 cm) this match deteriorates. Also the network averages show increasing deviation from the RMSM station for essentially two periods. For the period January–April, the RMSM station shows underestimation whereas the RMSM station overestimates the network average for the remaining period. Variability for both time series is relatively low at 20 cm depth and, actually, is much lower than variability indicated by the satellite-based time series. We note that similar patterns are indicated at 40 cm probe depth. Patterns, however, are more pronounced with much lower temporal variability for the probe-based time series. Both the RMSM station and network average time series underestimate the satellite-based time series for all days of the year. Therefore observations at 20 cm and 40 cm are not suitable for satellite validation purposes. Most suitable for satellite validation are the observations at 10 cm depth by the fair matches between the RMSM station, the network average and the satellite-based time series for the period August–November. A complicating factor to all comparisons is the period June–July where a pronounced decrease of moisture storage is indicated by the probe-based time series. This decrease only is poorly represented by the satellite with largest deviations at shallow probe depths (5 cm and 10 cm).

Further results on time series analysis are shown by Taylor's diagram [

The relative merits in terms of statistics for each test sample can be inferred from

We plotted the Taylor diagram for 5 and 10 cm depth following results from previous analysis. At both depths, correlation around 0.9 is found for the RMSM stations. For other time series, correlation varies from 0.33–0.45 and from 0.63–0.73 for 5 and 10 cm, respectively. At 5 cm, lowest RMSE (0.03 m^{3}·m^{−3}) is found for RMSM station that in case of other patterns varies from 0.05–0.06 m^{3}·m^{−3}. RMSE varies from 0.04–0.06 m^{3}·m^{−3} at 10 cm with lowest values for RMSM station and pixel average observations. The standard deviation of RMSM station at 5 and 10 cm (about 0.07 m^{3}·m^{−3} and 0.09 m^{3}·m^{−3} respectively) is larger than the network average observations at these depths which is indicated by the continuous arc near 0.06 m^{3}·m^{−3}. For other time series observations, lower and higher standard deviation than the network average is observed at 5 and 10 cm, respectively. Higher standard deviation of RMSM stations at 5 and 10 cm shows larger variation of amplitude than the network average observation.

In [

Results of our comprehensive analyses are based on widely accepted and independent methods that all indicate that field observations at 10 cm depth best match to the satellite observations. This outcome was somewhat surprising since penetration depth of the microwave signal commonly is considered to be less than 5 cm. We refer to [

Critical to applications of the temporal stability concept is that the sample size of observations should be sufficiently large to represent the natural variability of soil moisture. The minimum sampling time is identified by evaluating the progression of MRD and SD(MRD) values in the time dimension. In our study MRD and SD(MRD) values did not change markedly after 11 months and is only just within the length of the available time series that covered 12 month. To better substantiate on findings of the temporal stability concept we advocate usage of a much longer period.

Results of temporal stability analysis in this study showed that for each probe depth, a specific RMSM station can be identified. However, the identified RMSM station differs at each depth. Analysis indicated that for all depths, catchment MSM is well represented by the RMSM station. Based on Pearson's correlation analysis, we found that correlation in the time domain is much higher than in the space domain but appears plausible by the large inter-station distances. Application of the temporal stability concept, pearson's correlation analysis and results shown by Taylor's Diagram indicate that observations at 10 cm probe are most suited to be used for soil moisture satellite validation in the Maqu area. Results of application of the temporal stability concept to a time series of satellite images showed that a pixel indicting RMSM can be identified. This RMSM pixel, however, didn't overlay a RMSM station at any of the probe depths so we could not show that the RMSM pixel overlays a RMSM station. Results indicate that the AMSR-E VUA images have relatively low temporal variability as indicated by small values of MRD and SD(MRD). Values for the satellite pixels are relatively small and actually much smaller than probe-based MRD and SD(MRD) values at shallow depth (5 and 10 cm). Deviations are not systematic over the observation period so conclusions on bias effects are not drawn. A comparison between network averaged and image averaged time series shows that the satellite images in particular have difficulty to represent moisture conditions under dry conditions. Time series analysis showed that network average moisture contents best match with observation time series at 10 cm probe depth. This is also indicated in findings on the RMSM station where we showed that the 10 cm observation depth is best suited to represent temporal persistence (see

Based on the extensive but complementary analysis in this study, we conclude that probe observations at 10 cm depth are best suited to serve validation of the AMSR-E VUA images in Maqu area. We note that we compared observations directly so we ignored aspect of profile or root zone moisture. Further, probe network densities are unequal for respective depths so inter-comparison of correlation results rely on different samples which may have affected our findings. In this study, we report on a first application of the temporal stability concept to a series of satellite images. Results in this study show that the concept is very well applicable in satellite-based moisture assessments. We note that applicability to a time series of images should be tested more widely, particularly by considering profile soil moisture. Overall, we conclude that validation of satellite moisture products may benefit from application of the temporal stability concept. Applications should preferably be tested for more dense networks and larger number of satellite pixels.

The data collection for this study has been carried out under EU funded CEOP-AEGIS project in which Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences (CAREERI, CAS) and ITC (Faculty of Geo-Information Science and Earth Observation, University of Twente, Enschede, The Netherlands) are involved. The authors acknowledge Prof. Wen Jun of CAREERI, CAS for making data available. The main author also thanks Erasmus Mundus Mobility for Regional Asia (EMMA) and NED University of Engineering and Technology, Karachi, Pakistan for providing financial support to pursue his PhD study.

The authors declare no conflict of interest.

A Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) of Maqu Area. Station locations are indicated by various symbols. P1, P2,…..P15 represents pixel numbers. Stations selected for analysis are indicated by circles. The red box marks the pixels (

MRD plots at 5, 10, 20 and 40 cm depth. For each station the MRD is indicated by the small box. Whiskers indicate the standard deviation (SD) of the time series (SD(MRD)) for the year 2009. Station numbers refer to stations as shown in

Coefficients of determination (R^{2}) between daily averaged observations at the respective RMSM stations and daily averaged MSM of the remaining network stations.

Triangular matrix of Pearson correlation coefficient (

Triangular matrix of Pearson correlation coefficient [

Bar plot showing occurrence (%) for high, medium and low correlation at 5 cm, 10 cm, 20 cm and 40 cm depths. For high correlation |_{j}_{j}_{′}| > 0.7, for low correlation |_{j}_{j}_{′}| < 0.3.

Bar plot showing occurrence (%) for high, medium and low correlation at 5 cm, 10 cm, 20 cm and 40 cm depths. For high correlation |_{i}_{i}_{′}| > 0.7, for low correlation |_{i}_{i}_{′}| < 0.3.

MRD plot for the screened AMSR-E VUA pixels (descending overpass) Pixel numbers are shown in

Time series comparison of soil moisture observation from network average (

Taylor diagram illustrating statistics of the comparison between RMSM station, RMSM pixel, pixel average, pixel overlay on the RMSM station and the network average (the bench mark). The azimuthal angle represents correlation coefficient; radial distance represents standard deviation (m^{3}·m^{−3}) of the soil moisture time series and green contours represent RMSE (m^{3}·m^{−3}).

C1, N1, N2, N3, N14 | P8 |

N7 | P9 |

N8, N9, N10 | P10 |

C2, N5 | P13 |

N11, N12 | P14 |

No stations available | P15 |

Minimum (Min) and Maximum (Max) values of MRD and SD(MRD) at 5, 10, 20, 40, 80 cm depth at the Maqu network stations.

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5 | −51 | +36 | 87 | 8 | 36 | 26 |

10 | −34 | +34 | 68 | 5 | 18 | 13 |

20 | −13 | +20 | 33 | 5 | 15 | 10 |

40 | −19 | +23 | 42 | 8 | 13 | 5 |

80 | −12 | +14 | 26 | 5 | 10 | 5 |

MRD is Mean Relative Difference; SD(MRD) is standard deviation of the MRD.

SD(MRD) of the driest and the wettest stations/pixels at 5, 10, 20 and 40 cm depth.

| ||||
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5 | N9 | 14 | N11 | 16 |

10 | N9 | 13 | N5 | 15 |

20 | N10 | 8 | N5 | 9 |

40 | N1 | 9 | N5 | 8 |

- | P14 | 3 | P8 | 6 |