A non-linear Granger-causality framework to investigate climate-vegetation dynamics

Satellite Earth observation has led to the creation of global climate data records of many important environmental and climatic variables. These come in the form of multivariate time series with different spatial and temporal resolutions. Data of this kind provide new means to further unravel the influence of climate on vegetation dynamics. However, as advocated in this article, commonly used statistical methods are often too simplistic to represent complex climate-vegetation relationships due to linearity assumptions. Therefore, as an extension of linear Granger-causality analysis, we present a novel non-linear framework consisting of several components, such as data collection from various databases, time series decomposition techniques, feature construction methods, and predictive modelling by means of random forests. Experimental results on global data sets indicate that, with this framework, it is possible to detect non-linear patterns that are much less visible with traditional Granger-causality methods. In addition, we discuss extensive experimental results that highlight the importance of considering non-linear aspects of climate-vegetation dynamics

Assessment of apparent nonstationarity in time series of annual inflow, daily precipitation, and atmospheric circulation indices: A case study from southwest Western Australia

The southwest region of Western Australia has experienced a sustained sequence of low annual inflows to major water supply dams over the past 30 years. Until recently, the dominant interpretation of this phenomenon has been predicated on the existence of one or more sharp breaks (change or jump points), with inflows fluctuating around relatively constant levels between them. This paper revisits this interpretation. To understand the mechanisms behind the changes, we also analyze daily precipitation series at multiple sites in the vicinity and time series for several indices of regional atmospheric circulation that may be considered as drivers of regional precipitation. We focus on the winter half-year for the region (May to October) as up to 80% of annual precipitation occurs during this "season". We find that the decline in the annual inflow is in fact more consistent with a smooth declining trend than with a sequence of sharp breaks, the decline is associated with decreases both in the frequency of daily precipitation occurrence and in wet-day amounts, and the decline in regional precipitation is strongly associated with a marked decrease in moisture content in the lower troposphere, an increase in regionally averaged sea level pressure in the first half of the season, and intraseasonal changes in the regional north-south sea level pressure gradient. Overall, our approach provides an integrated understanding of the linkages between declining dam inflows, declining precipitation, and changes in regional atmospheric circulation that favor drier conditions

Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology

The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

Estimating causal networks in biosphere–atmosphere interaction with the PCMCI approach

Local meteorological conditions and biospheric activity are tightly coupled. Understanding these links is an essential prerequisite for predicting the Earth system under climate change conditions. However, many empirical studies on the interaction between the biosphere and the atmosphere are based on correlative approaches that are not able to deduce causal paths, and only very few studies apply causal discovery methods. Here, we use a recently proposed causal graph discovery algorithm, which aims to reconstruct the causal dependency structure underlying a set of time series. We explore the potential of this method to infer temporal dependencies in biosphere-atmosphere interactions. Specifically we address the following questions: How do periodicity and heteroscedasticity influence causal detection rates, i.e. the detection of existing and non-existing links? How consistent are results for noise-contaminated data? Do results exhibit an increased information content that justifies the use of this causal-inference method? We explore the first question using artificial time series with well known dependencies that mimic real-world biosphere-atmosphere interactions. The two remaining questions are addressed jointly in two case studies utilizing observational data. Firstly, we analyse three replicated eddy covariance datasets from a Mediterranean ecosystem at half hourly time resolution allowing us to understand the impact of measurement uncertainties. Secondly, we analyse global NDVI time series (GIMMS 3g) along with gridded climate data to study large-scale climatic drivers of vegetation greenness. Overall, the results confirm the capacity of the causal discovery method to extract time-lagged linear dependencies under realistic settings. The violation of the method's assumptions increases the likelihood to detect false links. Nevertheless, we consistently identify interaction patterns in observational data. Our findings suggest that estimating a directed biosphere-atmosphere network at the ecosystem level can offer novel possibilities to unravel complex multi-directional interactions. Other than classical correlative approaches, our findings are constrained to a few meaningful set of relations which can be powerful insights for the evaluation of terrestrial ecosystem models

Climatic change controls productivity variation in global grasslands.

Detection and identification of the impacts of climate change on ecosystems have been core issues in climate change research in recent years. In this study, we compared average annual values of the normalized difference vegetation index (NDVI) with theoretical net primary productivity (NPP) values based on temperature and precipitation to determine the effect of historic climate change on global grassland productivity from 1982 to 2011. Comparison of trends in actual productivity (NDVI) with climate-induced potential productivity showed that the trends in average productivity in nearly 40% of global grassland areas have been significantly affected by climate change. The contribution of climate change to variability in grassland productivity was 15.2-71.2% during 1982-2011. Climate change contributed significantly to long-term trends in grassland productivity mainly in North America, central Eurasia, central Africa, and Oceania; these regions will be more sensitive to future climate change impacts. The impacts of climate change on variability in grassland productivity were greater in the Western Hemisphere than the Eastern Hemisphere. Confirmation of the observed trends requires long-term controlled experiments and multi-model ensembles to reduce uncertainties and explain mechanisms

Soil erosion in the Alps : causes and risk assessment

The issue of soil erosion in the Alps has long been neglected due to the low economic value of the agricultural land. However, soil stability is a key parameter which affects ecosystem services like slope stability, water budgets (drinking water reservoirs as well as flood prevention), vegetation productivity, ecosystem biodiversity and nutrient production. In alpine regions, spatial estimates on soil erosion are difficult to derive because the highly heterogeneous biogeophysical structure impedes measurement of soil erosion and the applicability of soil erosion models. However, remote sensing and geographic information system (GIS) methods allow for spatial estimation of soil erosion by direct detection of erosion features and supply of input data for soil erosion models. Thus, the main objective of this work is to address the problem of soil erosion risk assessment in the Alps on catchment scale with remote sensing and GIS tools. Regarding soil erosion processes the focus is on soil erosion by water (here sheet erosion) and gravity (here landslides). For these two processes we address i) the monitoring and mapping of the erosion features and related causal factors ii) soil erosion risk assessment with special emphasis on iii) the validation of existing models for alpine areas. All investigations were accomplished in the Urseren Valley (Central Swiss Alps) where the valley slopes are dramatically affected by sheet erosion and landslides. For landslides, a natural susceptibility of the catchment has been indicated by bivariate and multivariate statistical analysis. Geology, slope and stream density are the most significant static landslide causal factors. Static factors are here defined as factors that do not change their attributes during the considered time span of the study (45 years), e.g. geology, stream network. The occurrence of landslides might be significantly increased by the combined effects of global climate and land use change. Thus, our hypothesis is that more recent changes in land use and climate affected the spatial and temporal occurrence of landslides. The increase of the landslide area of 92% within 45 years in the study site confirmed our hypothesis. In order to identify the cause for the trend in landslide occurrence time-series of landslide causal factors were analysed. The analysis revealed increasing trends in the frequency and intensity of extreme rainfall events and stocking of pasture animals. These developments presumably enhanced landslide hazard. Moreover, changes in land-cover and land use were shown to have affected landslide occurrence. For instance, abandoned areas and areas with recently emerging shrub vegetation show very low landslide densities. Detailed spatial analysis of the land use with GIS and interviews with farmers confirmed the strong influence of the land use management practises on slope stability. The definite identification and quantification of the impact of these non-stationary landslide causal factors (dynamic factors) on the landslide trend was not possible due to the simultaneous change of several factors. The consideration of dynamic factors in statistical landslide susceptibility assessments is still unsolved. The latter may lead to erroneous model predictions, especially in times of dramatic environmental change. Thus, we evaluated the effect of dynamic landslide causal factors on the validity of landslide susceptibility maps for spatial and temporal predictions. For this purpose, a logistic regression model based on data of the year 2000 was set up. The resulting landslide susceptibility map was valid for spatial predictions. However, the model failed to predict the landslides that occurred in a subsequent event. In order to handle this weakness of statistic landslide modelling a multitemporal approach was developed. It is based on establishing logistic regression models for two points in time (here 1959 and 2000). Both models could correctly classify >70% of the independent spatial validation dataset. By subtracting the 1959 susceptibility map from the 2000 susceptibility map a deviation susceptibility map was obtained. Our interpretation was that these susceptibility deviations indicate the effect of dynamic causal factors on the landslide probability. The deviation map explained 85% of new independent landslides occurring after 2000. Thus, we believe it to be a suitable tool to add a time element to a susceptibility map pointing to areas with changing susceptibility due to recently changing environmental conditions or human interactions. In contrast to landslides that are a direct threat to buildings and infrastructure, sheet erosion attracts less attention because it is often an unseen process. Nonetheless, sheet erosion may account for a major proportion of soil loss. Soil loss by sheet erosion is related to high spatial variability, however, in contrast to arable fields for alpine grasslands erosion damages are long lasting and visible over longer time periods. A crucial erosion triggering parameter that can be derived from satellite imagery is fractional vegetation cover (FVC). Measurements of the radiogenic isotope Cs-137, which is a common tracer for soil erosion, confirm the importance of FVC for soil erosion yield in alpine areas. Linear spectral unmixing (LSU), mixture tuned matched filtering (MTMF) and the spectral index NDVI are applied for estimating fractional abundance of vegetation and bare soil. To account for the small scale heterogeneity of the alpine landscape very high resolved multispectral QuickBird imagery is used. The performance of LSU and MTMF for estimating percent vegetation cover is good (r²=0.85, r²=0.71 respectively). A poorer performance is achieved for bare soil (r²=0.28, r²=0.39 respectively) because compared to vegetation, bare soil has a less characteristic spectral signature in the wavelength domain detected by the QuickBird sensor. Apart from monitoring erosion controlling factors, quantification of soil erosion by applying soil erosion risk models is done. The performance of the two established models Universal Soil Loss Equation (USLE) and Pan-European Soil Erosion Risk Assessment (PESERA) for their suitability to model erosion for mountain environments is tested. Cs-137 is used to verify the resulting erosion rates from USLE and PESERA. PESERA yields no correlation to measured Cs-137 long term erosion rates and shows lower sensitivity to FVC. Thus, USLE is used to model the entire study site. The LSU-derived FVC map is used to adapt the C factor of the USLE. Compared to the low erosion rates computed with the former available low resolution dataset (1:25000) the satellite supported USLE map shows “hotspots” of soil erosion of up to 16 t ha-1 a-1. In general, Cs-137 in combination with the USLE is a very suitable method to assess soil erosion for larger areas, as both give estimates on long-term soil erosion. Especially for inaccessible alpine areas, GIS and remote sensing proved to be powerful tools that can be used for repetitive measurements of erosion features and causal factors. In times of global change it is of crucial importance to account for temporal developments. However, the evaluation of the applied soil erosion risk models revealed that the implementation of temporal aspects, such as varying climate, land use and vegetation cover is still insufficient. Thus, the proposed validation strategies (spatial, temporal and via Cs-137) are essential. Further case studies in alpine regions are needed to test the methods elaborated for the Urseren Valley. However, the presented approaches are promising with respect to improve the monitoring and identification of soil erosion risk areas in alpine regions