We have carried out a comparison study for a set of benchmark problems which are relevant for convection in the Earth's mantle. The cases comprise steady isoviscous convection, variable viscosity convection and time-dependent convection with internal heating. We compare Nusselt numbers, velocity, temperature, heat-flow , topography and geoid data. Among the applied codes are finite-difference, finite-element and spectral methods. In a synthesis we give best estimates of the 'true' solutions and ranges of uncertainty. We recommend these data for the validation of convection codes in the future.

The current study applied a new approach for the interpolation and regionalization of observed precipitation series to a smaller spatial scale (0.125° by 0.125° grid) across the Upper Indus Basin (UIB), with appropriate adjustments for the orographic effect and changes in glacier storage. The approach is evaluated and validated through reverse hydrology, and is guided by observed flows and the available knowledge base. More specifically, the generated corrected precipitation data is validated by means of SWAT-modelled responses of the observed flows to the different input precipitation series (original and corrected ones). The results show that the SWAT-simulated flows using the corrected, regionalized precipitation series as input are much more in line with the observed flows than those using the uncorrected observed precipitation input for which significant underestimations are obtained.

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Abstract:Modeling the hydrologic responses to future changes of climate is important for improving adaptive water management. In the present application to the Zarrine River Basin (ZRB), with the major reach being the main inflow source of Lake Urmia (LU), firstly future daily temperatures and precipitation are predicted using two statistical downscaling methods: the classical statistical downscaling model (SDSM), augmented by a trend-preserving bias correction, and a two-step updated quantile mapping (QM) method. The general circulation models (GCM) input to SDSM are climate predictors of the Canadian Earth System Model (CanESM2) GCM under the representative concentration pathway (RCP) emission scenarios, RCP45 and RCP85, whereas that to the QM is provided by the most suitable of several Climate Model Intercomparison Project Phase 5 (CMIP5) GCMs under RCP60, in addition. The performances of the two downscaling methods are compared to each other for a past "future" period (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016) and the QM is found to be better and so is selected in the subsequent ZR streamflow simulations by means of the Soil and Water Assessment Tool (SWAT) hydrological model, calibrated and validated for the reference period . The impacts of climate change on the hydrologic response of the river basin, specifically the inflow to the Boukan Reservoir, the reservoir-dependable water release (DWR), are then compared for the three RCPs in the near-(2020-2038), middle-(2050-2068) and far-(2080-2098) future periods assuming (1) the "current" consumptive demand to be continued in the future, and (2) a more conservative "recommended" demand. A systematic future shortage of the available water is obtained for case (1) which can be mitigated somewhat for (2). Finally, the SWAT-predicted ZRB outflow is compared with the Montana-based estimated environmental flow of the ZR. The latter can successfully be sustained at good and fair levels for the near-and middle-future periods, but not so for the summer months of the far-future period, particularly, for RCP85.

This paper gives the essential results of numerical simulations on the stability, uniqueness and reliability of the solution for the 3-D seismic inverse problem for the determination of lateral velocity heterogeneities in the lithosphere. The starting point of the investigations is the well known and widely used 3-D inverse method of Aki, Christoffersson & Husebye (ACH method) for the inversion of teleseismic travel times. There are several approximations inherent in the construction of the method which may bias considerably the inverse solution obtained. These approximations are essentially: (1) the simplified block sampling which deteriorates the spatial resolution, and (2) the neglect of the lateral refraction at the vertical block boundaries. For the examination of the inherent approximations in the ACH method an exact 3-D ray tracing program has been developed which allows the calculation of theoretical travel times in an arbitrary laterally inhomogeneous media parameterized b y rectangular blocks. The numerical computations show that approximation (1) in the ACH method does not cause a significant degradation of the quality of the model reconstructed. Nevertheless for lateral heterogeneities of about 5-6 per cent contrast a systematic underestimation of the original perturbations of about 25 per cent is encountered. For remedy a non-linear inverse method has been developed which is based on the Levenberg-Marquardt (LM) algorithm. The computations with the LM method show that the systematic underestimate in the linear ACH method can be removed substantially. For investigating the statistical errors a non-linear F-test has been used which proves to give more conservative and reliable confidence regions than the formulae generally used for the calculation of the covariance of the inverse solution. On the other hand the confidence regions demonstrate also that non-linear inversion gives only a significant improvement with 95 per cent certainty if the statistical errors in the arrival-time data do not exceed 0.1-0.2 s.