Field-scale prediction of soil moisture patterns by means of a fuzzy c-means clustering algorithm, ancillary data, and sparse TDR measurements

Abstract:

Introduction

Soil moisture is a key state variable for many hydrological, biogeographical, geomorphological, and climatological processes. Many of them interact and the relationships between states and processes often show a nonlinear behavior (Rodriguez-Iturbe et al., 1991). Therefore, the spatial and temporal distribution of soil moisture are highly dynamic and itself has impact on other environmental variables (Legates et al., 2011).

For the hydrological cycle, the amount of water stored in the vadose zone is of critical importance because it controls for instance the partition of rain into an infiltration and a runoff component and influences the rate of evapotranspiration. The interplay of static (e.g. soil texture, topography) and dynamic (e.g. vegetation characteristics, climate) properties and the state of the system itself are responsible for the redistribution of water in the catchment. Therefore, the detection of the spatial structure of properties and states is of central importance because they show significant control over water-related surface and subsurface fluxes (Grayson et al., 1997). Because of its integrative character, a well-designed observation strategy for soil moisture dynamics can provide an improved understanding of the catchment inherent hydrological processes and the driving forces which lead to site-specific soil moisture patterns. For this reason, there is a great demand on high-resolution soil moisture data for many applications such as flood, drought and erosion prediction. Hence, soil moisture provides valuable information to improve the calibration and validation of physical parameterizations in land surface models.

The objective of this work is to develop a strategic sampling design to observe the spatial and temporal dynamics of soil moisture at the small catchment scale. Furthermore, we test a nonlinear estimation technique to predict soil moisture patterns from sparse TDR observations and to identify the relationship between environmental variables and soil moisture.

Study site

For our investigations we selected the Schaefertal (51°39'N, 11°03'E) as study site, which is a 144 ha catchment located in the Lower Harz Mountains in Central Germany. It has a V-shaped surface topography, with a first order stream in the valley. The site is characterized by four distinct landforms: 1) north-facing slope, 2) south-facing slope, both with gentle to moderate slopes (up to 6% - 20%) and intensively used for agriculture, 3) valley bottom utilized for pasture or meadow, and 4) topographically depressed areas (swales) disrupting the slopes one both sides. Average annual rainfall is 640 mm which is low compared to other low mountain-areas of Germany and due to the leeward position of the region (Ollesch et al., 2010). The catchment is underlain by Devonian greywacke and shale covered by a complex of periglacial layers with different fractions of silt and rock fragments (Altermann, 1985). The main soils are Cambisols and Luvisols on the arable land and Gleysols on the grassland sites in the valley bottom, in parts associated with a peaty soil layer (Borchardt, 1982). Due to the close collaboration with the University of Applied Sciences Magdeburg-Stendal which operates the catchment and which is part of the TERENO Harz/Central Geman Lowland Observatory (Zacharias et al., 2011), a multitude of sensor data is available. These encompass time lapse geophysical (EMI, gamma spectroscopy) as well as airborne and space borne remote sensing measurements (LiDAR, hyperspectral, thermal, SAR) which provide an ideal ground to develop and test our approach.

Soil moisture sampling and prediction approach

The recognition and integration of those landscape structures which are directly or indirectly linked to soil moisture is one of the key aspects in this research and is addressed by conducting a multi-sensor approach. This is planned in a stepwise procedure starting with a single sensor implementation and a successive integration of additional sensor data. The selection of the "right sensor for the right reason" is essential and the link to soil moisture is indispensable because they are used as proxy for specific factors controlling soil moisture, e.g. topography, soil texture or land use. In a first step, our stratified sampling design is based on topography only. Therefore, we used a digital elevation model (DEM) with one meter resolution to derive the four topographic attributes slope, elevation, SAGA topographic wetness index (Boehner, 2006) and potential incoming solar radiation. These attributes are spatially and continuously available for the entire catchment and represent key hydrological processes in a simplified way. For example, the surface slope influences the hydraulic gradient driving surface flows, the potential incoming solar radiation affects evapotranspiration, and the topographic wetness index defines zones of saturation (Western et al., 1999). Additionally, they integrate also some spatial soil information (e.g. texture, depth to water table) because the formation of soils is also affected by topography (Jenny, 1941; McBratney et al., 2003). As already stated, we are aware that topography is not the only controlling factor driving soil moisture dynamics. However, DEMs are widely available and it is rather to test as a first step in how far of soil moisture variability in the Schaefertal catchment can already be explained by topography.

To find an appropriate number of sampling locations, the fuzzy c-means (FCM) clustering technique was used to stratify the catchment, based on the four topographic attributes, into a specified number of similar landscape/structural units (SLUs). The FCM clustering technique ensures a joint interpretation of a multivariate continuum of spatially distributed data. The optimal classification for a selected number of c clusters is iteratively found such that the multivariate within-cluster variance is as small as possible (Burrough et al., 2000). One key question in all cluster applications is to find an appropriate number of classes. We addressed this issue considering FCM clustering as imaging technique projecting the four attribute maps onto a dimensionless fuzzy matrix describing the degree of membership of a sample in the attribute maps to a cluster (class) and an attribute matrix assigning mean values of the underlying four attributes to any cluster. Reconstructing the attribute maps from the fuzzy and the attribute matrix allows for quantification of informational loss during the clustering procedure. A simple L-curve analysis of informational loss over different number of clusters allows for the identification of an optimal number of classes. The fuzzy matrix of this optimal solution is then further analyzed for the identification of suitable TDR sample locations. Out of each class a minimum of one measurement point is then randomly selected to form a sparse set of sampling points. At each point, campaign based TDR measurements are conducted and represent the local soil moisture state based on the average of three replicate TDR measurements.

The proposed concept is based on the idea of Paasche et al. (2006) who used the FCM cluster analysis for estimating the spatial distribution of petrophysical parameters. This concept was refined and extended to predict soil moisture spatial patterns. This is done by calculating the cross product of the structural information obtained by the fuzzy c-means, stored in the fuzzy membership matrix, and the sparse TDR measurement points measured within each landscape unit at a specific sampling date. To assess the prediction accuracy of this nonlinear estimation technique we calculated the Nash-Sutcliffe Coefficient of Efficiency (Nash and Sutcliffe, 1970). Therefore, we randomly selected 44 additional sampling points throughout the whole catchment which are used as validation points.

Soil moisture pattern dynamics and prediction

With the FCM clustering technique we derived 30 landscape units for the Schaefertal catchment and chose 50 measurement locations. In combination with the 44 randomly selected validations points, a total of 94 monitoring points were established within the catchment. To collect volumetric soil moisture data, five TDR measurement (in 0-10 cm depth) campaigns were conducted in a period from April to October 2013 at five selected dates (T1 - T5) to represent different wetting states of the catchment. The first TDR measurement campaign was conducted on the 17 April right after the snow melt, followed by a second campaign after one week of drying, and a thirs after three weeks with a small amount of rain between the second and the third campaign. All of them represent a wet moisture state of the catchment. The fourth campaign was conducted on 25 September followed by the fifth (T5) after one week of drying, which both represent an intermediate moisture state of the catchment. The spatial and temporal dynamics of the five TDR measurement campaigns are displayed in Fig. 1. All five measurement dates show a valley-dependent pattern with higher soil moisture values in the valley bottom. However, the pattern for the wet moisture states (T1 - T3) are more pronounced and also show higher soil moisture values for the northern slope compared to the southern slope whereas the pattern for the intermediate states (T4 - T5) is more uniform.

Figure 1: Temporal and spatial distribution of TDR-measured soil moisture for five measurement dates in the Schaefertal catchment

To test if topography is sufficient to reproduce the observed soil moisture patterns, Nash-Sutcliffe efficiencies were calculated for the predicted and observed soil moisture values based on the 44 validation points. Nash-Sutcliffe efficiencies indicate that topography becomes increasingly important during the wet period and explains much of the soil moisture spatial variability. For the intermediate state (T4 -T5), the predictive power is poorer which indicates that other factors than topography (e.g. vegetation, texture) are crucially influencing soil moisture dynamics.

Our results show a switch between a wet and a dry state of soil moisture spatial patterns which is in confirmation with studies of Grayson et al. (1997). This can also be proven by calculating the Spearman rank correlation coefficient (Vachaud et al., 1985) which shows a high relationship between the wet dates (0.83-0.93), indicating a persistent pattern, and decreasing values (0.56-0.39) if we compare patterns for the wet and dry states which indicate that the system has reorganized.

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