Investigation of discrepancies in satellite rainfall estimates over Ethiopia

Tropical Applications of Meteorology Using Satellite and Ground-Based Observations (TAMSAT) rainfall estimates are used extensively across Africa for operational rainfall monitoring and food security applications; thus, regional evaluations of TAMSAT are essential to ensure its reliability. This study assesses the performance of TAMSAT rainfall estimates, along with the African Rainfall Climatology (ARC), version 2; the Tropical Rainfall Measuring Mission (TRMM) 3B42 product; and the Climate Prediction Center morphing technique (CMORPH), against a dense rain gauge network over a mountainous region of Ethiopia. Overall, TAMSAT exhibits good skill in detecting rainy events but underestimates rainfall amount, while ARC underestimates both rainfall amount and rainy event frequency. Meanwhile, TRMM consistently performs best in detecting rainy events and capturing the mean rainfall and seasonal variability, while CMORPH tends to overdetect rainy events. Moreover, the mean difference in daily rainfall between the products and rain gauges shows increasing underestimation with increasing elevation. However, the distribution in satellite–gauge differences demon- strates that although 75% of retrievals underestimate rainfall, up to 25% overestimate rainfall over all eleva- tions. Case studies using high-resolution simulations suggest underestimation in the satellite algorithms is likely due to shallow convection with warm cloud-top temperatures in addition to beam-filling effects in microwave- based retrievals from localized convective cells. The overestimation by IR-based algorithms is attributed to nonraining cirrus with cold cloud-top temperatures. These results stress the importance of understanding re- gional precipitation systems causing uncertainties in satellite rainfall estimates with a view toward using this knowledge to improve rainfall algorithms.

Open solar flux estimates from near-Earth measurements of the interplanetary magnetic field: comparison of the first two perihelion passes of the Ulysses spacecraft

Results from all phases of the orbits of the Ulysses spacecraft have shown that the magnitude of the radial component of the heliospheric field is approximately independent of heliographic latitude. This result allows the use of near- Earth observations to compute the total open flux of the Sun. For example, using satellite observations of the interplanetary magnetic field, the average open solar flux was shown to have risen by 29% between 1963 and 1987 and using the aa geomagnetic index it was found to have doubled during the 20th century. It is therefore important to assess fully the accuracy of the result and to check that it applies to all phases of the solar cycle. The first perihelion pass of the Ulysses spacecraft was close to sunspot minimum, and recent data from the second perihelion pass show that the result also holds at solar maximum. The high level of correlation between the open flux derived from the various methods strongly supports the Ulysses discovery that the radial field component is independent of latitude. We show here that the errors introduced into open solar flux estimates by assuming that the heliospheric field’s radial component is independent of latitude are similar for the two passes and are of order 25% for daily values, falling to 5% for averaging timescales of 27 days or greater. We compare here the results of four methods for estimating the open solar flux with results from the first and second perehelion passes by Ulysses. We find that the errors are lowest (1–5% for averages over the entire perehelion passes lasting near 320 days), for near-Earth methods, based on either interplanetary magnetic field observations or the aa geomagnetic activity index. The corresponding errors for the Solanki et al. (2000) model are of the order of 9–15% and for the PFSS method, based on solar magnetograms, are of the order of 13–47%. The model of Solanki et al. is based on the continuity equation of open flux, and uses the sunspot number to quantify the rate of open flux emergence. It predicts that the average open solar flux has been decreasing since 1987, as Correspondence to: M. Lockwood (m.lockwood@rl.ac.uk) is observed in the variation of all the estimates of the open flux. This decline combines with the solar cycle variation to produce an open flux during the second (sunspot maximum) perihelion pass of Ulysses which is only slightly larger than that during the first (sunspot minimum) perihelion pass.

The importance of vertical velocity variability for estimates of the indirect aerosol effects

The activation of aerosols to form cloud droplets is dependent upon vertical velocities whose local variability is not typically resolved at the GCM grid scale. Consequently, it is necessary to represent the subgrid-scale variability of vertical velocity in the calculation of cloud droplet number concentration. This study uses the UK Chemistry and Aerosols community model (UKCA) within the Hadley Centre Global Environmental Model (HadGEM3), coupled for the first time to an explicit aerosol activation parameterisation, and hence known as UKCA-Activate. We explore the range of uncertainty in estimates of the indirect aerosol effects attributable to the choice of parameterisation of the subgrid-scale variability of vertical velocity in HadGEM-UKCA. Results of simulations demonstrate that the use of a characteristic vertical velocity cannot replicate results derived with a distribution of vertical velocities, and is to be discouraged in GCMs. This study focuses on the effect of the variance (σw2) of a Gaussian pdf (probability density function) of vertical velocity. Fixed values of σw (spanning the range measured in situ by nine flight campaigns found in the literature) and a configuration in which σw depends on turbulent kinetic energy are tested. Results from the mid-range fixed σw and TKE-based configurations both compare well with observed vertical velocity distributions and cloud droplet number concentrations. The radiative flux perturbation due to the total effects of anthropogenic aerosol is estimated at −1.9 W m−2 with σw = 0.1 m s−1, −2.1 W m−2 with σw derived from TKE, −2.25 W m−2 with σw = 0.4 m s−1, and −2.3 W m−2 with σw = 0.7 m s−1. The breadth of this range is 0.4 W m−2, which is comparable to a substantial fraction of the total diversity of current aerosol forcing estimates. Reducing the uncertainty in the parameterisation of σw would therefore be an important step towards reducing the uncertainty in estimates of the indirect aerosol effects. Detailed examination of regional radiative flux perturbations reveals that aerosol microphysics can be responsible for some climate-relevant radiative effects, highlighting the importance of including microphysical aerosol processes in GCMs.

The impact of uncertain precipitation data on insurance loss estimates using a flood catastrophe model

Catastrophe risk models used by the insurance industry are likely subject to significant uncertainty, but due to their proprietary nature and strict licensing conditions they are not available for experimentation. In addition, even if such experiments were conducted, these would not be repeatable by other researchers because commercial confidentiality issues prevent the details of proprietary catastrophe model structures from being described in public domain documents. However, such experimentation is urgently required to improve decision making in both insurance and reinsurance markets. In this paper we therefore construct our own catastrophe risk model for flooding in Dublin, Ireland, in order to assess the impact of typical precipitation data uncertainty on loss predictions. As we consider only a city region rather than a whole territory and have access to detailed data and computing resources typically unavailable to industry modellers, our model is significantly more detailed than most commercial products. The model consists of four components, a stochastic rainfall module, a hydrological and hydraulic flood hazard module, a vulnerability module, and a financial loss module. Using these we undertake a series of simulations to test the impact of driving the stochastic event generator with four different rainfall data sets: ground gauge data, gauge-corrected rainfall radar, meteorological reanalysis data (European Centre for Medium-Range Weather Forecasts Reanalysis-Interim; ERA-Interim) and a satellite rainfall product (The Climate Prediction Center morphing method; CMORPH). Catastrophe models are unusual because they use the upper three components of the modelling chain to generate a large synthetic database of unobserved and severe loss-driving events for which estimated losses are calculated. We find the loss estimates to be more sensitive to uncertainties propagated from the driving precipitation data sets than to other uncertainties in the hazard and vulnerability modules, suggesting that the range of uncertainty within catastrophe model structures may be greater than commonly believed.

Methane emissions from cattle: estimates from short-term measurements using a Green Feed system compared with measurements obtained using respiration chambers or sulphur hexafluoride tracer

The Green Feed (GF) system (C-Lock Inc., Rapid City, USA) is used to estimate total daily methane emissions of individual cattle using short-term measurements obtained over several days. Our objective was to compare measurements of methane emission by growing cattle obtained using the GF system with measurements using respiration chambers (RC)or sulphur hexafluoride tracer (SF6). It was hypothesised that estimates of methane emission for individual animals and treatments would be similar for GF compared to RC or SF6 techniques. In experiment 1, maize or grass silage-based diets were fed to four growing Holstein heifers, whilst for experiment 2, four different heifers were fed four haylage treatments. Both experiments were a 4 × 4 Latin square design with 33 day periods. Green Feed measurements of methane emission were obtained over 7 days (days 22–28) and com-pared to subsequent RC measurements over 4 days (days 29–33). For experiment 3, 12growing heifers rotationally grazed three swards for 26 days, with simultaneous GF and SF6 measurements over two 4 day measurement periods (days 15–19 and days 22–26).Overall methane emissions (g/day and g/kg dry matter intake [DMI]) measured using GF in experiments 1 (198 and 26.6, respectively) and 2 (208 and 27.8, respectively) were similar to averages obtained using RC (218 and 28.3, respectively for experiment 1; and 209 and 27.7, respectively, for experiment 2); but there was poor concordance between the two methods (0.1043 for experiments 1 and 2 combined). Overall, methane emissions measured using SF6 were higher (P<0.001) than GF during grazing (186 vs. 164 g/day), but there was significant (P<0.01) concordance between the two methods (0.6017). There were fewer methane measurements by GF under grazing conditions in experiment 3 (1.60/day) com-pared to indoor measurements in experiments 1 (2.11/day) and 2 (2.34/day). Significant treatment effects on methane emission measured using RC and SF6 were not evident for GF measurements, and the ranking for treatments and individual animals differed using the GF system. We conclude that under our conditions of use the GF system was unable to detectsignificant treatment and individual animal differences in methane emissions that were identified using both RC and SF6techniques, in part due to limited numbers and timing ofmeasurements obtained. Our data suggest that successful use of the GF system is reliant on the number and timing of measurements obtained relative to diurnal patterns of methane emission.

Preliminary leaf area index estimates from airborne small footprint full-waveform LiDAR data

This study has compared preliminary estimates of effective leaf area index (LAI) derived from fish-eye lens photographs to those estimated from airborne full-waveform small-footprint LiDAR data for a forest dataset in Australia. The full-waveform data was decomposed and optimized using a trust-region-reflective algorithm to extract denser point clouds. LAI LiDAR estimates were derived in two ways (1) from the probability of discrete pulses reaching the ground without being intercepted (point method) and (2) from raw waveform canopy height profile processing adapted to small-footprint laser altimetry (waveform method) accounting for reflectance ratio between vegetation and ground. The best results, that matched hemispherical photography estimates, were achieved for the waveform method with a study area-adjusted reflectance ratio of 0.4 (RMSE of 0.15 and 0.03 at plot and site level, respectively). The point method generally overestimated, whereas the waveform method with an arbitrary reflectance ratio of 0.5 underestimated the fish-eye lens LAI estimates.

Advances in the stochastic modelling of satellite-derived rainfall estimates using a sparse calibration dataset

As satellite technology develops, satellite rainfall estimates are likely to become ever more important in the world of food security. It is therefore vital to be able to identify the uncertainty of such estimates and for end users to be able to use this information in a meaningful way. This paper presents new developments in the methodology of simulating satellite rainfall ensembles from thermal infrared satellite data. Although the basic sequential simulation methodology has been developed in previous studies, it was not suitable for use in regions with more complex terrain and limited calibration data. Developments in this work include the creation of a multithreshold, multizone calibration procedure, plus investigations into the causes of an overestimation of low rainfall amounts and the best way to take into account clustered calibration data. A case study of the Ethiopian highlands has been used as an illustration.

A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Assessing the performance of dynamical trajectory estimates

Estimating trajectories and parameters of dynamical systems from observations is a problem frequently encountered in various branches of science; geophysicists for example refer to this problem as data assimilation. Unlike as in estimation problems with exchangeable observations, in data assimilation the observations cannot easily be divided into separate sets for estimation and validation; this creates serious problems, since simply using the same observations for estimation and validation might result in overly optimistic performance assessments. To circumvent this problem, a result is presented which allows us to estimate this optimism, thus allowing for a more realistic performance assessment in data assimilation. The presented approach becomes particularly simple for data assimilation methods employing a linear error feedback (such as synchronization schemes, nudging, incremental 3DVAR and 4DVar, and various Kalman filter approaches). Numerical examples considering a high gain observer confirm the theory.

An Ensemble Smoother with Error Estimates

A smoother introduced earlier by van Leeuwen and Evensen is applied to a problem in which real obser vations are used in an area with strongly nonlinear dynamics. The derivation is new , but it resembles an earlier derivation by van Leeuwen and Evensen. Again a Bayesian view is taken in which the prior probability density of the model and the probability density of the obser vations are combined to for m a posterior density . The mean and the covariance of this density give the variance-minimizing model evolution and its errors. The assumption is made that the prior probability density is a Gaussian, leading to a linear update equation. Critical evaluation shows when the assumption is justified. This also sheds light on why Kalman filters, in which the same ap- proximation is made, work for nonlinear models. By reference to the derivation, the impact of model and obser vational biases on the equations is discussed, and it is shown that Bayes’ s for mulation can still be used. A practical advantage of the ensemble smoother is that no adjoint equations have to be integrated and that error estimates are easily obtained. The present application shows that for process studies a smoother will give superior results compared to a filter , not only owing to the smooth transitions at obser vation points, but also because the origin of features can be followed back in time. Also its preference over a strong-constraint method is highlighted. Further more, it is argued that the proposed smoother is more efficient than gradient descent methods or than the representer method when error estimates are taken into account

Evaluation of a polynya flux model by means of thermal infrared satellite estimates

We test the ability of a two-dimensional flux model to simulate polynya events with narrow open-water zones by comparing model results to ice-thickness and ice-production estimates derived from thermal infrared Moderate Resolution Imaging Spectroradiometer (MODIS) observations in conjunction with an atmospheric dataset. Given a polynya boundary and an atmospheric dataset, the model correctly reproduces the shape of an 11 day long event, using only a few simple conservation laws. Ice production is slightly overestimated by the model, owing to an underestimated ice thickness. We achieved best model results with the consolidation thickness parameterization developed by Biggs and others (2000). Observed regional discrepancies between model and satellite estimates might be a consequence of the missing representation of the dynamic of the thin-ice thickening (e.g. rafting). We conclude that this simplified polynya model is a valuable tool for studying polynya dynamics and estimating associated fluxes of single polynya events.

Independent uncertainty estimates for coefficient based sea surface temperature retrieval from the Along-Trck Scanning Radiometer instruments

We establish a methodology for calculating uncertainties in sea surface temperature estimates from coefficient based satellite retrievals. The uncertainty estimates are derived independently of in-situ data. This enables validation of both the retrieved SSTs and their uncertainty estimate using in-situ data records. The total uncertainty budget is comprised of a number of components, arising from uncorrelated (eg. noise), locally systematic (eg. atmospheric), large scale systematic and sampling effects (for gridded products). The importance of distinguishing these components arises in propagating uncertainty across spatio-temporal scales. We apply the method to SST data retrieved from the Advanced Along Track Scanning Radiometer (AATSR) and validate the results for two different SST retrieval algorithms, both at a per pixel level and for gridded data. We find good agreement between our estimated uncertainties and validation data. This approach to calculating uncertainties in SST retrievals has a wider application to data from other instruments and retrieval of other geophysical variables.

Uncertainties in tidally adjusted estimates of sea level rise flooding (bathtub model) for the Greater London

Sea-level rise (SLR) from global warming may have severe consequences for coastal cities, particularly when combined with predicted increases in the strength of tidal surges. Predicting the regional impact of SLR flooding is strongly dependent on the modelling approach and accuracy of topographic data. Here, the areas under risk of sea water flooding for London boroughs were quantified based on the projected SLR scenarios reported in Intergovernmental Panel on Climate Change (IPCC) fifth assessment report (AR5) and UK climatic projections 2009 (UKCP09) using a tidally-adjusted bathtub modelling approach. Medium- to very high-resolution digital elevation models (DEMs) are used to evaluate inundation extents as well as uncertainties. Depending on the SLR scenario and DEMs used, it is estimated that 3%–8% of the area of Greater London could be inundated by 2100. The boroughs with the largest areas at risk of flooding are Newham, Southwark, and Greenwich. The differences in inundation areas estimated from a digital terrain model and a digital surface model are much greater than the root mean square error differences observed between the two data types, which may be attributed to processing levels. Flood models from SRTM data underestimate the inundation extent, so their results may not be reliable for constructing flood risk maps. This analysis provides a broad-scale estimate of the potential consequences of SLR and uncertainties in the DEM-based bathtub type flood inundation modelling for London boroughs.