A disposition of interpolation techniques

A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated values, 3) incorporation of ancillary information, and 4) incorporation of process knowledge. The described methods include inverse distance weighting, nearest neighbour methods, geostatistical interpolation methods, Kalman filter methods, Bayesian Maximum Entropy methods, etc. The applicability of methods in aggregation (upscaling) and disaggregation (downscaling) is discussed. Software for interpolation is described. The application of interpolation techniques is illustrated in two case studies: temporal interpolation of indicators for ecological water quality, and spatio-temporal interpolation and aggregation of pesticide concentrations in Dutch surface waters. A valuable next step will be to construct a decision tree or decision support system, that guides the environmental scientist to easy-to-use software implementations that are appropriate to solve their interpolation problem. Validation studies are needed to assess the quality of interpolated values, and the quality of information on uncertainty provided by the interpolation method

Weighted ensemble analysis of extreme precipitation under climate change

The frequency or intensity of heavy precipitation has likely increased in North America since 1950s. In order to analyze climate change impacts on extreme precipitation events in Chicago area, historical (1961-2000) and projected (2046-2065, 2081-2100) daily precipitation data are calculated from 13 statistical downscaling general circulation models under 3 CMIP3 emission scenarios: A1B, A2 and B1, as well as from 17 stations in NCDC and CCPN rain gage network. Then precipitation events of different recurrence intervals are calculated through regional frequency analysis and based on average deviation of climate model estimates from observation estimates, tricube weight function is used to assign weights to climate model ensemble. This weight result is further applied to projected quantile estimates to derive weighted expected values and confidence intervals of future extreme precipitation events under different emission scenarios, these results are further compared with current available estimates from NOAA Atlas 14. Finally, maximum entropy method (MEM) is applied to assign weights and the results are compared with those from weighted ensemble method (WEM). It is found that intensity and the confidence intervals of heavy precipitation is likely to increase significantly for about 20% from now to 2050s under all emission scenarios (A1B>A2>B1), afterwards, this increase trend will slow down (B1>A1B>A2). As for the performance of expected value projection based on MEM, it can also provide accurate estimates with high computational efficiency

On the dynamic nature of hydrological similarity

The increasing diversity and resolution of spatially distributed data on terrestrial systems greatly enhance the potential of hydrological modeling. Optimal and parsimonious use of these data sources requires, however, that we better understand (a) which system characteristics exert primary controls on hydrological dynamics and (b) to what level of detail do those characteristics need to be represented in a model. In this study we develop and test an approach to explore these questions that draws upon information theoretic and thermodynamic reasoning, using spatially distributed topographic information as a straightforward example. Specifically, we subdivide a mesoscale catchment into 105 hillslopes and represent each by a two-dimensional numerical hillslope model. These hillslope models differ exclusively with respect to topography-related parameters derived from a digital elevation model (DEM); the remaining setup and meteorological forcing for each are identical. We analyze the degree of similarity of simulated discharge and storage among the hillslopes as a function of time by examining the Shannon information entropy. We furthermore derive a “compressed” catchment model by clustering the hillslope models into functional groups of similar runoff generation using normalized mutual information (NMI) as a distance measure. Our results reveal that, within our given model environment, only a portion of the entire amount of topographic information stored within a digital elevation model is relevant for the simulation of distributed runoff and storage dynamics. This manifests through a possible compression of the model ensemble from the entire set of 105 hillslopes to only 6 hillslopes, each representing a different functional group, which leads to no substantial loss in model performance. Importantly, we find that the concept of hydrological similarity is not necessarily time invariant. On the contrary, the Shannon entropy as measure for diversity in the simulation ensemble shows a distinct annual pattern, with periods of highly redundant simulations, reflecting coherent and organized dynamics, and periods where hillslopes operate in distinctly different ways. We conclude that the proposed approach provides a powerful framework for understanding and diagnosing how and when process organization and functional similarity of hydrological systems emerge in time. Our approach is neither restricted to the model nor to model targets or the data source we selected in this study. Overall, we propose that the concepts of hydrological systems acting similarly (and thus giving rise to redundancy) or displaying unique functionality (and thus being irreplaceable) are not mutually exclusive. They are in fact of complementary nature, and systems operate by gradually changing to different levels of organization in time

Ecohydrological Modeling in Agroecosystems: Examples and Challenges

Human societies are increasingly altering the water and biogeochemical cycles to both improve ecosystem productivity and reduce risks associated with the unpredictable variability of climatic drivers. These alterations, however, often cause large negative environmental consequences, raising the question as to how societies can ensure a sustainable use of natural resources for the future. Here we discuss how ecohydrological modeling may address these broad questions with special attention to agroecosystems. The challenges related to modeling the two‐way interaction between society and environment are illustrated by means of a dynamical model in which soil and water quality supports the growth of human society but is also degraded by excessive pressure, leading to critical transitions and sustained societal growth‐collapse cycles. We then focus on the coupled dynamics of soil water and solutes (nutrients or contaminants), emphasizing the modeling challenges, presented by the strong nonlinearities in the soil and plant system and the unpredictable hydroclimatic forcing, that need to be overcome to quantitatively analyze problems of soil water sustainability in both natural and agricultural ecosystems. We discuss applications of this framework to problems of irrigation, soil salinization, and fertilization and emphasize how optimal solutions for large‐scale, long‐term planning of soil and water resources in agroecosystems under uncertainty could be provided by methods from stochastic control, informed by physically and mathematically sound descriptions of ecohydrological and biogeochemical interactions

Copula-based statistical modelling of synoptic-scale climate indices for quantifying and managing agricultural risks in australia

Australia is an agricultural nation characterised by one of the most naturally diverse climates in the world, which translates into significant sources of risk for agricultural production and subsequent farm revenues. Extreme climatic events have been significantly affecting large parts of Australia in recent decades, contributing to an increase in the vulnerability of crops, and leading to subsequent higher risk to a large number of agricultural producers. However, attempts at better managing climate related risks in the agricultural sector have confronted many challenges. First, crop insurance products, including classical claim-based and index-based insurance, are among the financial implements that allow exposed individuals to pool resources to spread their risk. The classical claim-based insurance indemnifies according to a claim of crop loss from the insured customer, and so can easily manage idiosyncratic risk, which is the case where the loss occurs independently.Nevertheless, the existence of systemic weather risk (covariate risk), which is the spread of extreme events over locations and times (e.g., droughts and floods), has been identified as the main reason for the failure of private insurance markets, such as the classical multi-peril crop insurance, for agricultural crops. The index-based insurance is appropriate to handle systemic but not idiosyncratic risk. The indemnity payments of the index-based insurance are triggered by a predefined threshold of an index (e.g., rainfall), which is related to such losses. Since the covariate nature of a climatic event, it sanctions the insurers to predict losses and ascertain indemnifications for a huge number of insured customers across a wide geographical area. However, basis risk, which is related to the strength of the relationship between the predefined indices used to estimate the average loss by the insured community and the actual loss of insured assets by an individual, is a major barrier that hinders uptake of the index-based insurance. Clearly, the high basis risk, which is a weak relationship between the index and loss, destroys the willingness of potential customers to purchase this insurance product. Second, the impact of multiple synoptic-scale climate mode indices (e.g., Southern Oscillation Index (SOI) and Indian Ocean Index (IOD)) on precipitation and crop yield is not identical in different spatial locations and at different times or seasons across the Australian continent since the influence of large-scale climate heterogeneous over the different regions. The occurrence, role, and amplitude of synoptic-scale climate modes contributing to the variability of seasonal crop production have shifted in recent decades. These variables generally complicate the climate and crop yield relationship that cannot be captured by traditional modelling and analysis approaches commonly found in published agronomic literature such as linear regression. In addition, the traditional linear analysis is not able to model the nonlinear and asymmetric interdependence between extreme insurance losses, which may occur in the case of systemic risk. Relying on the linear method may lead to the problem that different behaviour may be observed from joint distributions, particularly in the upper and lower regions, with the same correlation coefficient. As a result, the likelihood of extreme insurance losses can be underestimated or overestimated that lead to inaccuracies in the pricing of insurance policies. Another alternative is the use of the multivariate normal distribution, where the joint distribution is uniquely defined using the marginal distributions of variables and their correlation matrix. However, phenomena are not always normally distributed in practice. It is therefore important to develop new, scientifically verified, strategic measures to solve the challenges as mentioned above in order to support mitigating the influences of the climate-related risk in the agricultural sector. Copulas provide an advanced statistical approach to model the joint distribution of multivariate random variables. This technique allows estimating the marginal distributions of individual variables independently with their dependence structures. It is clear that the copula method is superior to the conventional linear regression since it does not require variables have to be normally distributed and their correlation can be either linear or non-linear. This doctoral thesis therefore adopts the advanced copula technique within a statistical modelling framework that aims to model: (1) The compound influence of synoptic-scale climate indices (i.e., SOI and IOD) and climate variables (i.e., precipitation) to develop a probabilistic precipitation forecasting system where the integrated role of different factors that govern precipitation dynamics are considered; (2) The compound influence of synoptic-scale climate indices on wheat yield; (3) The scholastic interdependencies of systemic weather risks where potential adaptation strategies are evaluated accordingly; and (4) The risk-reduction efficiencies of geographical diversifications in wheat farming portfolio optimisation. The study areas are Australia’s agro-ecological (i.e., wheat belt) zones where major seasonal wheat and other cereal crops are grown. The results from the first and second objectives can be used for not only forecasting purposes but also understanding the basis risk in the case of pricing climate index-based insurance products. The third and fourth objectives assess the interactions of drought events across different locations and in different seasons and feasible adaptation tools. The findings of these studies can provide useful information for decision-makers in the agricultural sector. The first study found the significant relationship between SOI, IOD, and precipitation. The results suggest that spring precipitation in Australia, except for the western part, can be probabilistically forecasted three months ahead. It is more interesting that the combination of SOI and IOD as the predictors will improve the performance of the forecast model. Similarly, the second study indicated that the largescale climate indices could provide knowledge of wheat crops up to six months in advance. However, it is noted that the influence of different climate indices varies over locations and times. Furthermore, the findings derived from the third study demonstrated the spatio-temporally stochastic dependence of the drought events. The results also prove that time diversification is potentially more effective in reducing the systemic weather risk compared to spatially diversifying strategy. Finally, the fourth objective revealed that wheat-farming portfolio could be effectively optimised through the geographical diversification. The outcomes of this study will lead to the new application of advanced statistical tools that provide a better understanding of the compound influence of synoptic-scale climatic conditions on seasonal precipitation, and therefore on wheat crops in key regions over the Australian continent. Furthermore, a comprehensive analysis of systemic weather risks performed through advanced copula-statistical models can help improve and develop novel agricultural adaptation strategies in not only the selected study region but also globally, where climate extreme events pose a serious threat to the sustainability and survival of the agricultural industry. Finally, the evaluation of the effectiveness of diversification strategies implemented in this study reveals new evidence on whether the risk pooling methods could potentially mitigate climate risks for the agricultural sector and subsequently, help farmers in prior preparation for uncertain climatic events

A joint probability approach for the confluence flood frequency analysis

The flood frequency analysis at or nearby the confluence of two tributaries is of interest because it is necessary for the design of the highway drainage structures. However, The shortage of the hydrological data at the confluence point makes the flood estimation challenging. This thesis presents a practical procedure for the flood frequency analysis at the confluence of two streams by multivariate simulation of the annual peak flow of the tributaries based on joint probability and Monte Carlo simulation. Copulas are introduced to identify the joint probability. The results of two case studies are compared with the flood estimated by the univariate flood frequency analysis based on the observation data. The results are also compared with the ones by the National Flood Frequency program developed by United State Geological Survey. The results by the proposed model are very close to ones by the unvariate flood frequency analysis

stochastic rainfall analysis for storm tank performance evaluation

Abstract. Stormwater detention tanks are widely used for mitigating impacts of combined sewer overflows (CSO) from urban catchments into receiving water bodies. The optimal size of detention tanks depends on climate and sewer system behaviours and can be estimated by using derived distribution approaches. They are based on using a stochastic model to fit the statistical pattern of observed rainfall records and a urban hydrology model to transform rainfall in sewer discharge. A key issue is the identification of the optimal structure of the stochastic rainfall model. Point processes are frequently applied, where rainfall events are schematised through the occurrence of rectangular pulses, which are governed by rainfall descriptors. In the presented model these latter descriptors are the interevent time (duration of the dry period between consecutive storms), event rainfall depth and event rainfall duration. This paper focuses on the analytical derivation of the probability distribution of the number and volume of overflows from the storm tank to the receiving water body for different and non-standard shapes of the probability distribution for above mentioned descriptors. The proposed approach is applied to 2 different sites in Spain: Valencia and Santander, located on the Mediterranean and northern Atlantic coastline, respectively. For both cases, it turned out that Pareto and Gamma-2 probability distributions for rainfall depth and duration provided a better fit than the exponential model, widely used in previous studies. A comparison between the two climatic zones, humid and semiarid, respectively, proves the key role played by climatic conditions for storm detention tanks sizing