Geostatistical analysis of rainfall

Rainfall can be modeled as a spatially correlated random field superimposed on a background mean value; therefore, geostatistical methods are appropriate for the analysis of rain gauge data. Nevertheless, there are certain typical features of these data that must be taken into account to produce useful results, including the generally non-Gaussian mixed distribution, the inhomogeneity and low density of observations, and the temporal and spatial variability of spatial correlation patterns. Many studies show that rigorous geostatistical analysis performs better than other available interpolation techniques for rain gauge data. Important elements are the use of climatological variograms and the appropriate treatment of rainy and nonrainy areas. Benefits of geostatistical analysis for rainfall include ease of estimating areal averages, estimation of uncertainties, and the possibility of using secondary information (e.g., topography). Geostatistical analysis also facilitates the generation of ensembles of rainfall fields that are consistent with a given set of observations, allowing for a more realistic exploration of errors and their propagation in downstream models, such as those used for agricultural or hydrological forecasting. This article provides a review of geostatistical methods used for kriging, exemplified where appropriate by daily rain gauge data from Ethiopia.

The impact of uncertainty in satellite data on the assessment of flood inundation models

The performance of flood inundation models is often assessed using satellite observed data; however these data have inherent uncertainty. In this study we assess the impact of this uncertainty when calibrating a flood inundation model (LISFLOOD-FP) for a flood event in December 2006 on the River Dee, North Wales, UK. The flood extent is delineated from an ERS-2 SAR image of the event using an active contour model (snake), and water levels at the flood margin calculated through intersection of the shoreline vector with LiDAR topographic data. Gauged water levels are used to create a reference water surface slope for comparison with the satellite-derived water levels. Residuals between the satellite observed data points and those from the reference line are spatially clustered into groups of similar values. We show that model calibration achieved using pattern matching of observed and predicted flood extent is negatively influenced by this spatial dependency in the data. By contrast, model calibration using water elevations produces realistic calibrated optimum friction parameters even when spatial dependency is present. To test the impact of removing spatial dependency a new method of evaluating flood inundation model performance is developed by using multiple random subsamples of the water surface elevation data points. By testing for spatial dependency using Moran’s I, multiple subsamples of water elevations that have no significant spatial dependency are selected. The model is then calibrated against these data and the results averaged. This gives a near identical result to calibration using spatially dependent data, but has the advantage of being a statistically robust assessment of model performance in which we can have more confidence. Moreover, by using the variations found in the subsamples of the observed data it is possible to assess the effects of observational uncertainty on the assessment of flooding risk.

Superensembles of linear viscoelastic models of polymer melts

The idea of incorporating multiple models of linear rheology into a superensemble, to forge a consensus forecast from the individual model predictions, is investigated. The relative importance of the individual models in the so-called multimodel superensemble (MMSE) was inferred by evaluating their performance on a set of experimental training data, via nonlinear regression. The predictive ability of the MMSE model was tested by comparing its predictions on test data that were similar (in-sample) and dissimilar (out-of-sample) to the training data used in the calibration. For the in-sample forecasts, we found that the MMSE model easily outperformed the best constituent model. The presence of good individual models greatly enhanced the MMSE forecast, while the presence of some bad models in the superensemble also improved the MMSE forecast modestly. While the performance of the MMSE model on the out-of-sample training data was not as spectacular, it demonstrated the robustness of this approach.

Deriving global flood hazard maps of fluvial floods through a physical model cascade

Global flood hazard maps can be used in the assessment of flood risk in a number of different applications, including (re)insurance and large scale flood preparedness. Such global hazard maps can be generated using large scale physically based models of rainfall-runoff and river routing, when used in conjunction with a number of post-processing methods. In this study, the European Centre for Medium Range Weather Forecasts (ECMWF) land surface model is coupled to ERA-Interim reanalysis meteorological forcing data, and resultant runoff is passed to a river routing algorithm which simulates floodplains and flood flow across the global land area. The global hazard map is based on a 30 yr (1979–2010) simulation period. A Gumbel distribution is fitted to the annual maxima flows to derive a number of flood return periods. The return periods are calculated initially for a 25×25 km grid, which is then reprojected onto a 1×1 km grid to derive maps of higher resolution and estimate flooded fractional area for the individual 25×25 km cells. Several global and regional maps of flood return periods ranging from 2 to 500 yr are presented. The results compare reasonably to a benchmark data set of global flood hazard. The developed methodology can be applied to other datasets on a global or regional scale.

Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events

The development of NWP models with grid spacing down to 1 km should produce more realistic forecasts of convective storms. However, greater realism does not necessarily mean more accurate precipitation forecasts. The rapid growth of errors on small scales in conjunction with preexisting errors on larger scales may limit the usefulness of such models. The purpose of this paper is to examine whether improved model resolution alone is able to produce more skillful precipitation forecasts on useful scales, and how the skill varies with spatial scale. A verification method will be described in which skill is determined from a comparison of rainfall forecasts with radar using fractional coverage over different sized areas. The Met Office Unified Model was run with grid spacings of 12, 4, and 1 km for 10 days in which convection occurred during the summers of 2003 and 2004. All forecasts were run from 12-km initial states for a clean comparison. The results show that the 1-km model was the most skillful over all but the smallest scales (approximately <10–15 km). A measure of acceptable skill was defined; this was attained by the 1-km model at scales around 40–70 km, some 10–20 km less than that of the 12-km model. The biggest improvement occurred for heavier, more localized rain, despite it being more difficult to predict. The 4-km model did not improve much on the 12-km model because of the difficulties of representing convection at that resolution, which was accentuated by the spinup from 12-km fields.

Realism of rainfall in a very high-resolution regional climate model

The realistic representation of rainfall on the local scale in climate models remains a key challenge. Realism encompasses the full spatial and temporal structure of rainfall, and is a key indicator of model skill in representing the underlying processes. In particular, if rainfall is more realistic in a climate model, there is greater confidence in its projections of future change. In this study, the realism of rainfall in a very high-resolution (1.5 km) regional climate model (RCM) is compared to a coarser-resolution 12-km RCM. This is the first time a convection-permitting model has been run for an extended period (1989–2008) over a region of the United Kingdom, allowing the characteristics of rainfall to be evaluated in a climatological sense. In particular, the duration and spatial extent of hourly rainfall across the southern United Kingdom is examined, with a key focus on heavy rainfall. Rainfall in the 1.5-km RCM is found to be much more realistic than in the 12-km RCM. In the 12-km RCM, heavy rain events are not heavy enough, and tend to be too persistent and widespread. While the 1.5-km model does have a tendency for heavy rain to be too intense, it still gives a much better representation of its duration and spatial extent. Long-standing problems in climate models, such as the tendency for too much persistent light rain and errors in the diurnal cycle, are also considerably reduced in the 1.5-km RCM. Biases in the 12-km RCM appear to be linked to deficiencies in the representation of convection.

Evaluation of Earth system models using modern and palaeo-observations: the state-of-the-art

Earth system models are increasing in complexity and incorporating more processes than their predecessors, making them important tools for studying the global carbon cycle. However, their coupled behaviour has only recently been examined in any detail, and has yielded a very wide range of outcomes, with coupled climate-carbon cycle models that represent land-use change simulating total land carbon stores by 2100 that vary by as much as 600 Pg C given the same emissions scenario. This large uncertainty is associated with differences in how key processes are simulated in different models, and illustrates the necessity of determining which models are most realistic using rigorous model evaluation methodologies. Here we assess the state-of-the-art with respect to evaluation of Earth system models, with a particular emphasis on the simulation of the carbon cycle and associated biospheric processes. We examine some of the new advances and remaining uncertainties relating to (i) modern and palaeo data and (ii) metrics for evaluation, and discuss a range of strategies, such as the inclusion of pre-calibration, combined process- and system-level evaluation, and the use of emergent constraints, that can contribute towards the development of more robust evaluation schemes. An increasingly data-rich environment offers more opportunities for model evaluation, but it is also a challenge, as more knowledge about data uncertainties is required in order to determine robust evaluation methodologies that move the field of ESM evaluation from "beauty contest" toward the development of useful constraints on model behaviour.

Toward seamless prediction: calibration of climate change projections using seasonal forecasts

The CWRF is developed as a climate extension of the Weather Research and Forecasting model (WRF) by incorporating numerous improvements in the representation of physical processes and integration of external (top, surface, lateral) forcings that are crucial to climate scales, including interactions between land, atmosphere, and ocean; convection and microphysics; and cloud, aerosol, and radiation; and system consistency throughout all process modules. This extension inherits all WRF functionalities for numerical weather prediction while enhancing the capability for climate modeling. As such, CWRF can be applied seamlessly to weather forecast and climate prediction. The CWRF is built with a comprehensive ensemble of alternative parameterization schemes for each of the key physical processes, including surface (land, ocean), planetary boundary layer, cumulus (deep, shallow), microphysics, cloud, aerosol, and radiation, and their interactions. This facilitates the use of an optimized physics ensemble approach to improve weather or climate prediction along with a reliable uncertainty estimate. The CWRF also emphasizes the societal service capability to provide impactrelevant information by coupling with detailed models of terrestrial hydrology, coastal ocean, crop growth, air quality, and a recently expanded interactive water quality and ecosystem model. This study provides a general CWRF description and basic skill evaluation based on a continuous integration for the period 1979– 2009 as compared with that of WRF, using a 30-km grid spacing over a domain that includes the contiguous United States plus southern Canada and northern Mexico. In addition to advantages of greater application capability, CWRF improves performance in radiation and terrestrial hydrology over WRF and other regional models. Precipitation simulation, however, remains a challenge for all of the tested models.

A traceable physical calibration of the vertical advection-diffusion equation for modelling ocean heat uptake

The classic vertical advection-diffusion (VAD) balance is a central concept in studying the ocean heat budget, in particular in simple climate models (SCMs). Here we present a new framework to calibrate the parameters of the VAD equation to the vertical ocean heat balance of two fully-coupled climate models that is traceable to the models’ circulation as well as to vertical mixing and diffusion processes. Based on temperature diagnostics, we derive an effective vertical velocity w∗ and turbulent diffusivity k∗ for each individual physical process. In steady-state, we find that the residual vertical velocity and diffusivity change sign in mid-depth, highlighting the different regional contributions of isopycnal and diapycnal diffusion in balancing the models’ residual advection and vertical mixing. We quantify the impacts of the time-evolution of the effective quantities under a transient 1%CO2 simulation and make the link to the parameters of currently employed SCMs.

A Spatial-Temporal Downscaling Approach To Construction Of Rainfall Intensity-Duration-Frequency Relations In The Context Of Climate Change

This paper proposes a spatial-temporal downscaling approach to construction of the intensity-duration-frequency (IDF) relations at a local site in the context of climate change and variability. More specifically, the proposed approach is based on a combination of a spatial downscaling method to link large-scale climate variables given by General Circulation Model (GCM) simulations with daily extreme precipitations at a site and a temporal downscaling procedure to describe the relationships between daily and sub-daily extreme precipitations based on the scaling General Extreme Value (GEV) distribution. The feasibility and accuracy of the suggested method were assessed using rainfall data available at eight stations in Quebec (Canada) for the 1961-2000 period and climate simulations under four different climate change scenarios provided by the Canadian (CGCM3) and UK (HadCM3) GCM models. Results of this application have indicated that it is feasible to link sub-daily extreme rainfalls at a local site with large-scale GCM-based daily climate predictors for the construction of the IDF relations for present (1961-1990) and future (2020s, 2050s, and 2080s) periods at a given site under different climate change scenarios. In addition, it was found that annual maximum rainfalls downscaled from the HadCM3 displayed a smaller change in the future, while those values estimated from the CGCM3 indicated a large increasing trend for future periods. This result has demonstrated the presence of high uncertainty in climate simulations provided by different GCMs. In summary, the proposed spatial-temporal downscaling method provided an essential tool for the estimation of extreme rainfalls that are required for various climate-related impact assessment studies for a given region.

Parameterization of bio-optical models for estimating chlorophyll-a concentration in a tropical eutrophic reservoir

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analysis of the impact of rainfall assimilation during LBA atmospheric mesoscale missions in Southwest Amazon

The assimilation of satellite estimated precipitation data can be used as an efficient tool to improve the analysis of rainfall generated by numerical models of weather forecast. The system of data assimilation used in this study is cumulus parameterization inversion based on the Kuo scheme. Reanalysis were performed using the field experiment data of the LBA Project (WETAMC and DRYtoWET-AMC), where it was possible to verify an improvement in the simulations results, since the data assimilation corrects the position and the intensity of rainfall in the numerical model. (C) 2012 Elsevier B.V. All rights reserved.

Variabilità spaziale dei parametri di modelli afflussi-deflussi

L’invarianza spaziale dei parametri di un modello afflussi-deflussi può rivelarsi una soluzione pratica e valida nel caso si voglia stimare la disponibilità di risorsa idrica di un’area. La simulazione idrologica è infatti uno strumento molto adottato ma presenta alcune criticità legate soprattutto alla necessità di calibrare i parametri del modello. Se si opta per l’applicazione di modelli spazialmente distribuiti, utili perché in grado di rendere conto della variabilità spaziale dei fenomeni che concorrono alla formazione di deflusso, il problema è solitamente legato all’alto numero di parametri in gioco. Assumendo che alcuni di questi siano omogenei nello spazio, dunque presentino lo stesso valore sui diversi bacini, è possibile ridurre il numero complessivo dei parametri che necessitano della calibrazione. Si verifica su base statistica questa assunzione, ricorrendo alla stima dell’incertezza parametrica valutata per mezzo di un algoritmo MCMC. Si nota che le distribuzioni dei parametri risultano in diversa misura compatibili sui bacini considerati. Quando poi l’obiettivo è la stima della disponibilità di risorsa idrica di bacini non strumentati, l’ipotesi di invarianza dei parametri assume ancora più importanza; solitamente infatti si affronta questo problema ricorrendo a lunghe analisi di regionalizzazione dei parametri. In questa sede invece si propone una procedura di cross-calibrazione che viene realizzata adottando le informazioni provenienti dai bacini strumentati più simili al sito di interesse. Si vuole raggiungere cioè un giusto compromesso tra lo svantaggio derivante dall’assumere i parametri del modello costanti sui bacini strumentati e il beneficio legato all’introduzione, passo dopo passo, di nuove e importanti informazioni derivanti dai bacini strumentati coinvolti nell’analisi. I risultati dimostrano l’utilità della metodologia proposta; si vede infatti che, in fase di validazione sul bacino considerato non strumentato, è possibile raggiungere un buona concordanza tra le serie di portata simulate e osservate.

Calibration of River Gauge at Afdeyu Research Station, Eritrea: A study conducted by MOA NARI and SLM

Afdeyu Station is one of the few river gauging stations in the highlands of Eritrea where daily measurements are taken. As a result of damages, the station was refurbished, and the cross section of the gauge was changed to have better control of minimal runoff. The gauge therefore had to be re-calibrated. This publication documents this process and also provides the new calibration curve, based on extensive field work carried out in the rainy season 2009

Radiocarbon dating of modern peat profiles: Pre- and post-bomb C-14 variations in the construction of age-depth models

We present studies of 9 modern (up to 400-yr-old) peat sections from Slovenia, Switzerland, Austria, Italy, and Finland. Precise radiocarbon dating of modern samples is possible due to the large bomb peak of atmospheric 14C concentration in 1963 and the following rapid decline in the 14C level. All the analyzed 14C profiles appeared concordant with the shape of the bomb peak of atmospheric 14C concentration, integrated over some time interval with a length specific to the peat section. In the peat layers covered by the bomb peak, calendar ages of individual peat samples could be determined almost immediately, with an accuracy of 23 yr. In the pre-bomb sections, the calendar ages of individual dated samples are determined in the form of multi-modal probability distributions of about 300 yr wide (about AD 16501950). However, simultaneous use of the post-bomb and pre-bomb 14C dates, and lithological information, enabled the rejection of most modes of probability distributions in the pre-bomb section. In effect, precise age-depth models of the post-bomb sections have been extended back in time, into the wiggly part of the 14C calibration curve.