Bias Correction Scheme Research Articles

Application of a statistical post-processing technique to a gridded, operational, air quality forecast

An automated air quality forecast bias correction scheme based on the short-term persistence of model bias with respect to recent observations is described. The scheme has been implemented in the operational Met Office five day regional air quality forecast for the UK. It has been evaluated against routine hourly pollution observations for a year-long hindcast. The results demonstrate the value of the scheme in improving performance. For the first day of the forecast the post-processing reduces the bias from 7.02 to 0.53 μg m−3 for O3, from −4.70 to −0.63 μg m−3 for NO2, from −4.00 to −0.13 μg m−3 for PM2.5 and from −7.70 to −0.25 μg m−3 for PM10. Other metrics also improve for all species. An analysis of the variation of forecast skill with lead-time is presented and demonstrates that the post-processing increases forecast skill out to five days ahead.

Effect of Bias Correction of Satellite-Rainfall Estimates on Runoff Simulations at the Source of the Upper Blue Nile

Results of numerous evaluation studies indicated that satellite-rainfall products are contaminated with significant systematic and random errors. Therefore, such products may require refinement and correction before being used for hydrologic applications. In the present study, we explore a rainfall-runoff modeling application using the Climate Prediction Center-MORPHing (CMORPH) satellite rainfall product. The study area is the Gilgel Abbay catchment situated at the source basin of the Upper Blue Nile basin in Ethiopia, Eastern Africa. Rain gauge networks in such area are typically sparse. We examine different bias correction schemes applied locally to the CMORPH product. These schemes vary in the degree to which spatial and temporal variability in the CMORPH bias fields are accounted for. Three schemes are tested: space and time-invariant, time-variant and spatially invariant, and space and time variant. Bias-corrected CMORPH products were used to calibrate and drive the Hydrologiska Byråns Vattenbalansavdelning (HBV) rainfall-runoff model. Applying the space and time-fixed bias correction scheme resulted in slight improvement of the CMORPH-driven runoff simulations, but in some instances caused deterioration. Accounting for temporal variation in the bias reduced the rainfall bias by up to 50%. Additional improvements were observed when both the spatial and temporal variability in the bias was accounted for. The rainfall bias was found to have a pronounced effect on model calibration. The calibrated model parameters changed significantly when using rainfall input from gauges alone, uncorrected, and bias-corrected CMORPH estimates. Changes of up to 81% were obtained for model parameters controlling the stream flow volume.

The Influence of Frequency Shifts in Microwave Sounder Channels on NWP Analyses and Forecasts

Abstract The sensitivity of numerical weather prediction (NWP) analysis and forecast accuracies with respect to frequency shifts in microwave passbands is quantified through a series of observing system experiments using the ECMWF Integrated Forecast System. First, a parameterization is developed to describe the form and magnitude of the brightness temperature errors arising from frequency shifts in Advanced Microwave Sounding Unit-A (AMSU-A) channels 4–10 and Microwave Humidity Sounder (MHS) channels 3–5. Observing system experiments are then run in which realistic synthetic brightness temperature errors are added to AMSU-A observations for various assumptions about the magnitude of a frequency shift, using the parameterization derived previously. A large negative impact on forecast quality is found when a 20-MHz frequency shift is introduced in experiments using a static bias-correction scheme. Although the degradation in forecast scores is reduced by using a variational bias-correction scheme, it remains around 7%–14% (relative) in RMS 6-h forecast errors for temperature and geopotential. Frequency shifts of 5 MHz or greater give rise to a measurable degradation of the forecast even when the variational correction scheme is used. Only low-frequency shifts (of ~1.5 MHz) are found to have a neutral impact on forecasts. Hence, the value of 1.5 MHz can be regarded as an upper limit below which frequency shifts do not degrade forecasts for the key tropospheric and lower-stratospheric temperature sounding channels in a microwave sounding mission. Calculations show that frequency shift is less problematic for 183-GHz humidity sounding channels due to the symmetric positioning of passbands relative to the 183-GHz absorption line. For these channels a passband center frequency stability of 10 MHz is adequate.

Multi-year objective analyses of warm season ground-level ozone and PM<sub>2.5</sub> over North America using real-time observations and Canadian operational air quality models

Abstract. Multi-year objective analyses (OA) on a high spatiotemporal resolution for the warm season period (1 May to 31 October) for ground-level ozone and for fine particulate matter (diameter less than 2.5 microns (PM2.5)) are presented. The OA used in this study combines model outputs from the Canadian air quality forecast suite with US and Canadian observations from various air quality surface monitoring networks. The analyses are based on an optimal interpolation (OI) with capabilities for adaptive error statistics for ozone and PM2.5 and an explicit bias correction scheme for the PM2.5 analyses. The estimation of error statistics has been computed using a modified version of the Hollingsworth–Lönnberg (H–L) method. The error statistics are "tuned" using a χ2 (chi-square) diagnostic, a semi-empirical procedure that provides significantly better verification than without tuning. Successful cross-validation experiments were performed with an OA setup using 90% of data observations to build the objective analyses and with the remainder left out as an independent set of data for verification purposes. Furthermore, comparisons with other external sources of information (global models and PM2.5 satellite surface-derived or ground-based measurements) show reasonable agreement. The multi-year analyses obtained provide relatively high precision with an absolute yearly averaged systematic error of less than 0.6 ppbv (parts per billion by volume) and 0.7 μg m−3 (micrograms per cubic meter) for ozone and PM2.5, respectively, and a random error generally less than 9 ppbv for ozone and under 12 μg m−3 for PM2.5. This paper focuses on two applications: (1) presenting long-term averages of OA and analysis increments as a form of summer climatology; and (2) analyzing long-term (decadal) trends and inter-annual fluctuations using OA outputs. The results show that high percentiles of ozone and PM2.5 were both following a general decreasing trend in North America, with the eastern part of the United States showing the most widespread decrease, likely due to more effective pollution controls. Some locations, however, exhibited an increasing trend in the mean ozone and PM2.5, such as the northwestern part of North America (northwest US and Alberta). Conversely, the low percentiles are generally rising for ozone, which may be linked to the intercontinental transport of increased emissions from emerging countries. After removing the decadal trend, the inter-annual fluctuations of the high percentiles are largely explained by the temperature fluctuations for ozone and to a lesser extent by precipitation fluctuations for PM2.5. More interesting is the economic short-term change (as expressed by the variation of the US gross domestic product growth rate), which explains 37% of the total variance of inter-annual fluctuations of PM2.5 and 15% in the case of ozone.

Radio Occultation Observations as Anchor Observations in Numerical Weather Prediction Models and Associated Reduction of Bias Corrections in Microwave and Infrared Satellite Observations

AbstractSatellite radiance measurements are used daily at numerical weather prediction (NWP) centers around the world, providing a significant positive impact on weather forecast skill. Owing to the existence of systematic errors, either in the observations, instruments, and/or forward models, which can be larger than the signal, the use of infrared or microwave radiances in data assimilation systems requires significant bias corrections. As most bias-correction schemes do not correct for biases that exist in the model forecasts, the model needs to be grounded by an unbiased observing system. These reference measurements, also known as “anchor observations,” prevent a drift of the model to its own climatology and associated biases, thus avoiding a spurious drift of the observation bias corrections.This paper shows that the assimilation of global positioning system (GPS) radio occultation (RO) observations over a 3-month period in an operational NWP system results in smaller, more accurate bias corrections in infrared and microwave observations, resulting in an overall more effective use of satellite radiances and a larger number of radiance observations that pass quality control. A full version of the NCEP data assimilation system is used to evaluate the results on the bias corrections for the High Resolution Infrared Radiation Sounder-3 (HIRS-3) on NOAA-17 and the Advanced Microwave Sounding Unit-A (AMSU-A) on NOAA-15 in an operational environment.

Improving Ensemble-Based Quantitative Precipitation Forecasts for Topography-Enhanced Typhoon Heavy Rainfall over Taiwan with a Modified Probability-Matching Technique

Abstract In this paper, a modified probability-matching technique is developed for ensemble-based quantitative precipitation forecasts (QPFs) associated with landfalling typhoons over Taiwan. The main features of this technique include a resampling of the ensemble realizations, a rainfall pattern adjustment, and a bias correction. Using this technique, a synthetic ensemble is created for the purpose of rainfall prediction from a large-size (32 members), low-resolution (36 km) ensemble and a small-size (8 members), high-resolution (4 km) ensemble. The rainfall pattern is adjusted based on the precipitation distribution of the 36- and 4-km ensembles. A bias-correction scheme is then applied to remove the known systematic bias from the resampled 4-km ensemble realizations as part of the probability-matching procedure. The modified probability-matching scheme is shown to substantially reduce or eliminate the intrinsic model rainfall bias and to provide better QPF guidance. The encouraging results suggest that this modified probability-matching technique is a useful tool for the QPF of the topography-enhanced typhoon heavy rainfall over Taiwan using ensemble forecasts at dual resolutions.

Bias-corrected short-range Member-to-Member ensemble forecasts of reservoir inflow

• We develop a short-term ensemble reservoir inflow forecasting system. • The ensemble attempts to sample all sources of uncertainty in the modeling chain. • Increasing the diversity of the ensemble greatly improves ensemble quality. • Bias correction of ensemble members offers significant additional improvement. • For the flashy case study basin, only recent errors are important in bias correction. A Member-to-Member ensemble forecasting system is developed for inflows to hydroelectric reservoirs that incorporates multiple numerical weather prediction models and multiple distributed hydrological models linked by a variety of downscaling schemes. Each hydrological model uses multiple differently-optimized parameter sets and begins each daily forecast from several different initial conditions. The ensemble thereby attempts to sample all sources of error in the modeling chain. The importance of sampling all sources of error is illustrated by comparing this ensemble with an ensemble comprised of single ‘best’ parameterization for each hydrological model. Degree-of-mass-balance bias correction schemes trained using data windows of varying lengths are applied to the individual ensemble members. Based on examination of various verification metrics, we determine that a bias corrector that uses a linearly-weighted combination of past errors calculated over a three-day moving window is able to significantly improve forecast quality for the flashy case study watershed in southwestern British Columbia, Canada. Incorporation of all sources of modeling uncertainty is found to greatly improve ensemble resolution and discrimination. The full potential for these improvements using ensembles is only realized after removal of bias.

The effect of spatially uniform and non-uniform precipitation bias correction methods on improving NEXRAD rainfall accuracy for distributed hydrologic modeling

In order to improve the accuracy of rainfall estimates from next generation radar (NEXRAD) uncertainties, data assimilation technique is performed by considering NEXRAD and available rain gauges which can be used to assimilate spatially uniform Multisensor Precipitation Estimator (MPE) scheme and non-uniform (based on rainfall interpolation and bias interpolation) NEXRAD bias estimations during a storm event by Kalman filtering. Even though NEXRAD provides a better spatial representation of rainfall variability than rain gauge information, it suffers from uncertainties and biases due to Z–R (reflectivity–rainfall) conversion method and limitation of available rain gauge information for NEXRAD bias correction in a particular river basin. Analysis of correcting NEXRAD bias rainfall with three different bias correction schemes is described in this study. The prediction accuracy of the STORE DHM (Storage Released based Distributed Hydrologic Model) simulations is also evaluated by using three different NEXRAD bias corrected rainfall inputs. The Upper Wabash River (17,907 km2) and the Upper Cumberland River (38,160 km2) basins are selected as the study areas to evaluate rainfall input sensitivity on different spatial characteristics. Use of spatially non-uniform NEXRAD bias correction schemes results has better rainfall and prediction accuracy compared to that of spatially uniform NEXRAD bias correction rainfall.

Exposing XBT bias in the Atlantic sector of the Southern Ocean

Hydrographic data from three research cruises, occupying the GoodHope line in the Atlantic sector of the Southern Ocean, are used to identify and quantify Expendable Bathythermograph (XBT) temperature biases. A set of 148 collocated XBT and CTD stations, separated by a maximum distance of <12.5nm and <10h, are used in this study. A subset of these comparisons is also investigated.This subset consists of 24 simultaneous pairs where the XBT and CTD stations are within 2.5nm and 2h of one another. These simultaneous pairs are extremely rare in XBT bias experiments and provide data set to assess, in deeper detail, the behaviour of the bias. The net bias, which is a product of both the depth offset and the pure thermal bias, is investigated with depth per frontal zone for both the collocated and simultaneous comparisons and found to be on the whole positive, meaning warmer XBT readings compared to the CTD values at each depth. The total mean bias for all collocated pairs was found to be 0.101±0.024°C, and for the simultaneous subset the net bias had a mean value of 0.130±0.064°C. An investigation into the magnitude of the depth offset was also undertaken, exposing generally positive depth biases, thereby indicating an overestimation of depth by the fall rate equation. A sizeable variation in bias between frontal zones is observed, along with an expected increase of net bias in regions of steeper temperature gradient. The contribution of the pure thermal bias is explored and found to be comparatively small yet still sizeable (mean bias=0.053±0.063°C). Results found in this study further support the hypothesis of the regional dependence of the XBT fall rate on water temperature, and thus water viscosity. In addition, results obtained here highlight the need to develop an XBT bias correction scheme specifically appropriate to the Southern Ocean.

Preliminary evaluations of FGOALS-g2 for decadal predictions

The Flexible Global Ocean-Atmosphere-Land System model, Grid-point Version 2 (FGOALS-g2) for decadal predictions, is evaluated preliminarily, based on sets of ensemble 10-year hindcasts that it has produced. The results show that the hindcasts were more accurate in decadal variability of SST and surface air temperature (SAT), particularly in that of Nino3.4 SST and China regional SAT, than the second sample of the historical runs for 20th-century climate (the control) by the same model. Both the control and the hindcasts represented the global warming well using the same external forcings, but the control overestimated the warming. The hindcasts produced the warming closer to the observations. Performance of FGOALS-g2 in hindcasts benefits from more realistic initial conditions provided by the initialization run and a smaller model bias resulting from the use of a dynamic bias correction scheme newly developed in this study. The initialization consists of a 61-year nudging-based assimilation cycle, which follows on the control run on 01 January 1945 with the incorporation of observation data of upper-ocean temperature and salinity at each integration step in the ocean component model, the LASG IAP Climate System Ocean Model, Version 2 (LICOM2). The dynamic bias correction is implemented at each step of LICOM2 during the hindcasts to reduce the systematic biases existing in upper-ocean temperature and salinity by incorporating multi-year monthly mean increments produced in the assimilation cycle. The effectiveness of the assimilation cycle and the role of the correction scheme were assessed prior to the hindcasts.

Atmospheric carbon dioxide retrieved from the Greenhouse gases Observing SATellite (GOSAT): Comparison with ground‐based TCCON observations and GEOS‐Chem model calculations

We retrieved column‐averaged dry air mole fractions of atmospheric carbon dioxide () from backscattered short‐wave infrared (SWIR) sunlight measured by the Japanese Greenhouse gases Observing SATellite (GOSAT). Over two years of retrieved from GOSAT is compared with inferred from collocated SWIR measurements by seven ground‐based Total Carbon Column Observing Network (TCCON) stations. The average difference between GOSAT and TCCON for individual TCCON sites ranges from −0.87 ppm to 0.77 ppm with a mean value of 0.1 ppm and standard deviation of 0.56 ppm. We find an average bias between all GOSAT and TCCON retrievals of −0.20 ppm with a standard deviation of 2.26 ppm and a correlation coefficient of 0.75. One year of was retrieved from GOSAT globally, which was compared to global 3‐D GEOS‐Chem chemistry transport model calculations. We find that the latitudinal gradient, seasonal cycles, and spatial variability of GOSAT and GEOS‐Chem agree well in general with a correlation coefficient of 0.61. Regional differences between GEOS‐Chem model calculations and GOSAT observations are typically less than 1 ppm except for the Sahara and central Asia where a mean difference between 2 to 3 ppm is observed, indicating regional biases in the GOSAT retrievals unobserved by the current TCCON network. Using a bias correction scheme based on linear regression these regional biases are significantly reduced, approaching the required accuracy for surface flux inversions.

Interannual variability of carbon monoxide emission estimates over South America from 2006 to 2010

We present the first inverse modeling study to estimate CO emissions constrained by both surface and satellite observations. Our 4D‐Var system assimilates National Oceanic and Atmospheric Administration Earth System Research Laboratory (NOAA/ESRL) Global Monitoring Division (GMD) surface and Measurements Of Pollution In The Troposphere (MOPITT) satellite observations jointly by fitting a bias correction scheme. This approach leads to the identification of a positive bias of maximum 5 ppb in MOPITT column‐averaged CO mixing ratios in the remote Southern Hemisphere (SH). The 4D‐Var system is used to estimate CO emissions over South America in the period 2006–2010 and to analyze the interannual variability (IAV) of these emissions. We infer robust, high spatial resolution CO emission estimates that show slightly smaller IAV due to fires compared to the Global Fire Emissions Database (GFED3) prior emissions. South American dry season (August and September) biomass burning emission estimates amount to 60, 92, 42, 16 and 93 Tg CO/yr for 2006 to 2010, respectively. Moreover, CO emissions probably associated with pre‐harvest burning of sugar cane plantations in São Paulo state are underestimated in current inventories by 50–100%. We conclude that climatic conditions (such as the widespread drought in 2010) seem the most likely cause for the IAV in biomass burning CO emissions. However, socio‐economic factors (such as the growing global demand for soy, beef and sugar cane ethanol) and associated deforestation fires, are also likely as drivers for the IAV of CO emissions, but are difficult to link directly to CO emissions.

Assimilation of F-16 Special Sensor Microwave Imager/Sounder Data in the NCEP Global Forecast System

Abstract The Special Sensor Microwave Imager/Sounder (SSMIS) on board the Defense Meteorological Satellite Program (DMSP) F-16 satellite is the first conically scanning sounding instrument that provides information on atmospheric temperature and water vapor profiles. The SSMIS data were preprocessed by the Naval Research Laboratory (NRL) using its Unified Preprocessor Package (UPP) and then distributed to the numerical weather prediction centers by the Fleet Numerical Meteorology and Oceanography Center (FNMOC). This dataset was assimilated into the Global Forecast System (GFS) using gridpoint statistical interpolation (GSI). The initial assimilation of the SSMIS data into the GFS did not improve the medium-range (5–7 days) forecast skill. The SSMIS bias (O-B) still changes with location and time after the GSI bias-correction scheme is implemented. This bias characteristic is related to residual calibration errors in the correction of the SSMIS antenna emission and warm target contamination. The large O-B standard deviation is probably due to the large instrument noise in the SSMIS UPP data. The large O-B and its standard deviation for several surface sensitive channels are also caused by uncertainty in surface emissivity. In this study, a new scheme is developed to remove regionally dependent bias using a weekly composite O-B. The SSMIS noise is reduced through a Gaussian function filter. A new emissivity database for snow and sea ice is developed for the SSMIS surface sensitive channels. After applying these algorithms, the quality of the SSMIS low-atmospheric sounding (LAS) data is improved; the surface-sensitive channels can be effectively assimilated, and the impacts of SSMIS LAS data on the medium-range forecast in the GFS are positive and similar to those from Advanced Microwave Sounding Unit-A (AMSU-A) data.

Comparing optimized CO emission estimates using MOPITT or NOAA surface network observations

This paper compares two global inversions to estimate carbon monoxide (CO) emissions for 2004. Either surface flask observations from the National Oceanic and Atmospheric Administration Earth System Research Laboratory (NOAA/ESRL) Global Monitoring Division (GMD) or CO total columns from the Measurement of Pollution in the Troposphere (MOPITT) instrument are assimilated in a 4D‐Var framework. Inferred emission estimates from the two inversions are consistent over the Northern Hemisphere (NH). For example, both inversions increase anthropogenic CO emissions over Europe (from 46 to 94 Tg CO/yr) and Asia (from 222 to 420 Tg CO/yr). In the Southern Hemisphere (SH), three important findings are reported. First, due to their different vertical sensitivity, the stations‐only inversion increases SH biomass burning emissions by 108 Tg CO/yr more than the MOPITT‐only inversion. Conversely, the MOPITT‐only inversion results in SH natural emissions (mainly CO from oxidation of NMVOCs) that are 185 Tg CO/yr higher compared to the stations‐only inversion. Second, MOPITT‐only derived biomass burning emissions are reduced with respect to the prior which is in contrast to previous (inverse) modeling studies. Finally, MOPITT derived total emissions are significantly higher for South America and Africa compared to the stations‐only inversion. This is likely due to a positive bias in the MOPITT V4 product. This bias is also apparent from validation with surface stations and ground‐truth FTIR columns. Our results show that a combined inversion is promising in the NH. However, implementation of a satellite bias correction scheme is essential to combine both observational data sets in the SH.

Improved point estimation for the Kumaraswamy distribution

We develop nearly unbiased estimators for the Kumaraswamy distribution proposed by Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 46 (1980), pp. 79–88], which has considerable attention in hydrology and related areas. We derive modified maximum-likelihood estimators that are bias-free to second order. As an alternative to the analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. We conduct Monte Carlo simulations in order to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates.

Estimating second-order Volterra system parameters from noisy measurements based on an LMS variant or an errors-in-variables method

This paper deals with the identification of a nonlinear SISO system modelled by a second-order Volterra series expansion when both the input and the output are disturbed by additive white Gaussian noises. Two methods are proposed. Firstly, we present an unbiased on-line approach based on the LMS. It includes a bias correction scheme which requires the variance of the input additive noise. Secondly, we suggest solving the identification problem as an errors-in-variables issue, by means of the so-called Frisch scheme. Although its computational cost is high, this approach has the advantage of estimating the Volterra kernels and the variances of both the additive noises and the input signal, even if the signal-to-noise ratios at the input and the output are low.

Evaluation of several model error schemes in the EnKF assimilation: Applied to Argo profiles in the Pacific Ocean

[1] The efficacy of several model error schemes in the Ensemble Kalman Filter (EnKF) data assimilation is investigated through a series of sensitivity experiments, in which the Argo and other in situ temperature and salinity profiles are assimilated into an ocean general circulation model (OGCM) for the Pacific Ocean. Different schemes for combining the additive inflation, multiplicative inflation, one-step bias correction and two-stage bias correction are evaluated in the framework of the EnKF. Experimental results indicate that the additive inflation is the key technique that can maintain ensemble spread in an adequate range. When sufficient observations are available, the assimilation system with additive inflation scheme can efficiently reduce both model bias and random errors. The combination of additive inflation and multiplicative inflation can further improve the performance of the assimilation system, in particular when the additive inflation underestimates model error. The bias correction schemes, the one-step method and the persistent bias method are effective in reducing the model bias only within a relatively short initial assimilation period and in some regions. Further improvement from the bias correction schemes is not evident as the assimilation period increases.

Towards a bias correction of the AVHRR Pathfinder SST data from 1985 to 1998 using ATSR

There are many sea surface temperature (SST) datasets derived from various satellite instruments with different characteristics in terms of orbit, coverage, retrieval, calibration, accuracy and measurement type. This paper presents the results of a project to combine SSTs from two instruments: the Along-Track Scanning Radiometer (ATSR) SSTs and the Advanced Very High Resolution Radiometer (AVHRR) Pathfinder SSTs. The dual-view nature of the (A)ATSR series of radiometers enables high-quality sea surface temperatures to be retrieved. These SSTs are ideal for using as a reference in order to bias-adjust the AVHRR series of instruments. In addition a method to correct for aerosol effects in the AVHRR SSTs is employed using aerosol optical depth from the Total Ozone Mapping Spectrometer. The method enables positive characteristics of both datasets to be combined to provide a dataset of potentially high-quality, long time-series, large data coverage satellite sea surface temperatures for climate monitoring purposes.An AVHRR SST dataset at ¼ degree spatial resolution with associated systematic biases and uncertainties is produced for climate research covering the period 1985 to 1998. The method is used to produce improved AVHRR SSTs for the period 1991 to the present (when the ATSRs are available) and additionally the method can be used to estimate biases on AVHRR SSTs prior to the first ATSR launch (1985 to 1991).The bias-correction has the effect of reducing an observed cool bias in the AVHRR SSTs, relative to the Hadley Centre Sea-Ice and Sea Surface Temperature dataset (HadISST), especially in cases of high volcanic and Saharan dust aerosol. The time-series indicates that the bias correction scheme is effective during the 1990s at decreasing the cool bias in the AVHRR SSTs. The scheme is especially effective in times of high atmospheric volcanic aerosol levels such as the period following the Mount Pinatubo eruption in 1991.

Observation errors in all‐sky data assimilation

AbstractThis article examines the first‐guess (FG) departures of microwave imager radiances assimilated in all‐sky conditions (i.e. clear, cloudy and precipitating). Agreement between FG and observations is good in clear skies, with error standard deviations around 2 K, but in heavy cloud or precipitation errors increase to 20 K. The forecast model is not good at predicting cloud and precipitation with exactly the right intensity or location. This leads to apparently non‐Gaussian behaviour, both heteroscedasticity, i.e. an increase in error with cloud amount, and boundedness, i.e. the size of errors is close to the geophysical range of the observations, which runs from clear to fully cloudy. However, the dependence of FG departure standard deviations on the mean cloud amount is predictable. Using this dependence to normalise the FG departures gives an error distribution that is close to Gaussian. Thus if errors are treated correctly, all‐sky observations can be assimilated successfully under the assumption of Gaussianity on which assimilation systems are based. This ‘symmetric’ error model can be used to provide a robust threshold quality‐control check and to determine the size of observation errors for all‐sky assimilation. In practice, however, this ‘observation’ error is being used to account for the model's difficulty in forecasting cloud, which really comes from errors in the background and in the forecast model. Hence in future it will be necessary to improve the representation of background and model error. Separately, symmetric cloud amount is recommended as a predictor for bias correction schemes, avoiding the sampling problems associated with ‘asymmetric’ predictors like the FG cloud amount. Copyright © 2011 Royal Meteorological Society

Potential Use of Surface-Sensitive Microwave Observations Over Land in Numerical Weather Prediction

This paper describes several sensitivity studies carried out with the French global 4-D-Var system to check its ability to assimilate surface-sensitive observations over land from the Special Sensor Microwave Imager (SSM/I). As well as a sound knowledge of land-surface parameters, the assimilation of SSM/I observations requires effective rain-detection and bias-correction algorithms. Three sensitivity components are hence analyzed with a special emphasis on the land-surface emissivity at SSM/I frequencies estimated from satellite observations. Several rain algorithms were tested to reject cloudy/rainy observations over land, and the bias-correction scheme was adapted to improve its performance over land and sea surfaces. Once these problems have been outlined, a global 4-D-Var assimilation experiment which assimilates SSM/I observations over land surfaces was run and compared with a control experiment. The impact on forecast scores has been found to be globally positive. Nevertheless, the very high sensitivity of SSM/I to each of the three components presented in this study is characterized by opposite effects that, once clustered together, lead to some residual biases over land due to their combined effects.