A common task in environmental studies is to determine toxicant concentrations at which a certain proportion (typically 95 per cent) of the biological species is protected. Extrapolation techniques need to be employed for small sample sizes. By definition, our interest focuses on the lower tail of the NOEC (no observed effect concentration) distribution, which is very sensitive to the choice of the underlying distribution. In this paper we investigate the use of the three‐parameter Burr Type III distribution because of its flexibility and ease‐of‐use. The Constrained Maximum Likelihood (CML) method was used to estimate parameters. Collinearity between parameter estimates was overcome by reparameterisation techniques. As an alternative to the computation of adjustment factors, we estimate the lower confidence limits of percentile estimates using the Delta‐method. When the NOEC sample sizes are small, we employ Bootstrapping, a computer intensive technique. Our technique is easily extended to mixtures of the three‐parameter Burr type III distributions, which can be used to model multimodal distributions. Copyright © 2000 John Wiley & Sons, Ltd.

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This paper provides a statistically unified method for modelling trends in groundwater levels for a national project that aims to predict areas at risk from salinity in 2020. It was necessary to characterize the trends in groundwater levels in thousands of boreholes that have been monitored by Agriculture Western Australia throughout the south-west of Western Australia over the last 10 years. The approach investigated in the present paper uses segmented regression with constraints when the number of change points is unknown. For each segment defined by change points, the trend can be described by a linear trend possibly superimposed on a periodic response. Four different types of change point are defined by constraints on the model parameters to cope with different patterns of change in groundwater levels. For a set of candidate change points provided by the user, a modified Akaike information criterion is used for model selection. Model parameters can be estimated by multiple linear regression. Some typical examples are presented to demonstrate the performance of the approach.

Investigation on the climatic effects of irrigation is of great significance to fully understand the impact of water management on the Earth's environment and hydrological cycle. To comprehensively explore the effects of irrigation across different climatic regions over China, we propose a novel combined irrigation scheme (including dynamic and fixed irrigation schemes) into the Weather Research and Forecasting (WRF)‐Noah‐mosaic model. Two experiments (with and without irrigation) are designed to simulate the impacts of irrigation over China on regional climate. As irrigation increases the latent heat flux but decreases the sensible heat flux and surface temperature, and the magnitudes of corresponding change are highly dependent on the irrigation amounts and irrigation fraction, the evaporative cooling effects significantly reduce the warm bias over extensive irrigation area during crop growing seasons. Meanwhile, irrigation increases soil moisture during both irrigated and non‐irrigated seasons. Compared with the dynamic irrigation scheme, the fixed irrigation scheme results in relatively higher subsurface runoffs due to the continuous infiltration. In addition, the irrigation‐induced changes on precipitation during spring (March–May) are weaker than that during summer (June–August). The opposed effects of irrigation cooling and wetting on generating convective precipitation, and the irrigation‐induced changes in large‐scale circulation jointly give rise to the heterogeneous changes of precipitation. Besides, the subgrid‐scale irrigation scheme can capture the climatic effects of irrigation in some grids where the dominant land use types are not cropland, indicating that in mesoscale simulation, climate model coupled with subgrid‐scale irrigation scheme may improve climate variables trends attribution studies.