Correlated observation errors in data assimilation

Data assimilation provides techniques for combining observations and prior model forecasts to create initial conditions for numerical weather prediction (NWP). The relative weighting assigned to each observation in the analysis is determined by its associated error. Remote sensing data usually has correlated errors, but the correlations are typically ignored in NWP. Here, we describe three approaches to the treatment of observation error correlations. For an idealized data set, the information content under each simplified assumption is compared with that under correct correlation specification. Treating the errors as uncorrelated results in a significant loss of information. However, retention of an approximated correlation gives clear benefits.

Sampling uncertainties in surface radiation budget calculations in RADAGAST

In the Radiative Atmospheric Divergence Using ARM Mobile Facility GERB and AMMA Stations (RADAGAST) project we calculate the divergence of radiative flux across the atmosphere by comparing fluxes measured at each end of an atmospheric column above Niamey, in the African Sahel region. The combination of broadband flux measurements from geostationary orbit and the deployment for over 12 months of a comprehensive suite of active and passive instrumentation at the surface eliminates a number of sampling issues that could otherwise affect divergence calculations of this sort. However, one sampling issue that challenges the project is the fact that the surface flux data are essentially measurements made at a point, while the top-of-atmosphere values are taken over a solid angle that corresponds to an area at the surface of some 2500 km2. Variability of cloud cover and aerosol loading in the atmosphere mean that the downwelling fluxes, even when averaged over a day, will not be an exact match to the area-averaged value over that larger area, although we might expect that it is an unbiased estimate thereof. The heterogeneity of the surface, for example, fixed variations in albedo, further means that there is a likely systematic difference in the corresponding upwelling fluxes. In this paper we characterize and quantify this spatial sampling problem. We bound the root-mean-square error in the downwelling fluxes by exploiting a second set of surface flux measurements from a site that was run in parallel with the main deployment. The differences in the two sets of fluxes lead us to an upper bound to the sampling uncertainty, and their correlation leads to another which is probably optimistic as it requires certain other conditions to be met. For the upwelling fluxes we use data products from a number of satellite instruments to characterize the relevant heterogeneities and so estimate the systematic effects that arise from the flux measurements having to be taken at a single point. The sampling uncertainties vary with the season, being higher during the monsoon period. We find that the sampling errors for the daily average flux are small for the shortwave irradiance, generally less than 5 W m−2, under relatively clear skies, but these increase to about 10 W m−2 during the monsoon. For the upwelling fluxes, again taking daily averages, systematic errors are of order 10 W m−2 as a result of albedo variability. The uncertainty on the longwave component of the surface radiation budget is smaller than that on the shortwave component, in all conditions, but a bias of 4 W m−2 is calculated to exist in the surface leaving longwave flux.

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

The accuracy of Doppler radar wind retrievals using insects as targets

Insect returns from the UK's Doppler weather radars were collected in the summers of 2007 and 2008, to ascertain their usefulness in providing information about boundary layer winds. Such observations could be assimilated into numerical weather prediction models to improve forecasts of convective showers before precipitation begins. Significant numbers of insect returns were observed during daylight hours on a number of days through this period, when they were detected at up to 30 km range from the radars, and up to 2 km above sea level. The range of detectable insect returns was found to vary with time of year and temperature. There was also a very weak correlation with wind speed and direction. Use of a dual-polarized radar revealed that the insects did not orient themselves at random, but showed distinct evidence of common orientation on several days, sometimes at an angle to their direction of travel. Observation minus model background residuals of wind profiles showed greater bias and standard deviation than that of other wind measurement types, which may be due to the insects' headings/airspeeds and to imperfect data extraction. The method used here, similar to the Met Office's procedure for extracting precipitation returns, requires further development as clutter contamination remained one of the largest error contributors. Wind observations derived from the insect returns would then be useful for data assimilation applications.

A new set of orthogonal patterns in weather and climate: Optimally interpolated patterns.

A new spectral-based approach is presented to find orthogonal patterns from gridded weather/climate data. The method is based on optimizing the interpolation error variance. The optimally interpolated patterns (OIP) are then given by the eigenvectors of the interpolation error covariance matrix, obtained using the cross-spectral matrix. The formulation of the approach is presented, and the application to low-dimension stochastic toy models and to various reanalyses datasets is performed. In particular, it is found that the lowest-frequency patterns correspond to largest eigenvalues, that is, variances, of the interpolation error matrix. The approach has been applied to the Northern Hemispheric (NH) and tropical sea level pressure (SLP) and to the Indian Ocean sea surface temperature (SST). Two main OIP patterns are found for the NH SLP representing respectively the North Atlantic Oscillation and the North Pacific pattern. The leading tropical SLP OIP represents the Southern Oscillation. For the Indian Ocean SST, the leading OIP pattern shows a tripole-like structure having one sign over the eastern and north- and southwestern parts and an opposite sign in the remaining parts of the basin. The pattern is also found to have a high lagged correlation with the Niño-3 index with 6-months lag.

Pb-210-Ra-226 and Ra-228-Th-232 systematics in young arc lavas: implications for magma degassing and ascent rates

New data show that island arc rocks have (Pb-210/Ra-226)(o) ratios which range from as low as 0.24 up to 2.88. In contrast, (Ra-22S/Th-232) appears always within error of I suggesting that the large Ra-226-excesses observed in arc rocks were generated more than 30 years ago. This places a maximum estimate on melt ascent velocities of around 4000 m/year and provides further confidence that the Ra-226 excesses reflect deep (source) processes rather than shallow level alteration or seawater contamination. Conversely, partial melting must have occurred more than 30 years prior to eruption. The Pb-210 deficits are most readily explained by protracted magma degassing. Using published numerical models, the data suggest that degassing occurred continuously for periods up to several decades just prior to eruption but no link with eruption periodicity was found. Longer periods are required if degassing is discontinuous, less than 100% efficient or if magma is recharged or stored after degassing. The long durations suggest much of this degassing occurs at depth with implications for the formation of hydrothermal and copper-porphyry systems. A suite of lavas erupted in 1985-1986 from Sangeang Api volcano in the Sunda arc are characterised by deficits of Pb-210 relative to Ra-226 from which 6-8 years of continuous Rn-222 degassing would be inferred from recent numerical models. These data also form a linear (Pb-210)/Pb-(Ra-226)/Pb array which might be interpreted as a 71-year isochron. However, the array passes through the origin suggesting displacement downwards from the equiline in response to degassing and so the slope of the array is inferred not to have any age significance. Simple modelling shows that the range of (Ra-226)/Pb ratios requires thousands of years to develop consistent with differentiation occurring in response to cooling at the base of the crust. Thus, degassing post-dated, and was not responsible for magma differentiation. The formation, migration and extraction of gas bubbles must be extremely efficient in mafic magma whereas the higher viscosity of more siliceous magmas retards the process and can lead to Pb-210 excesses. A possible negative correlation between (Pb-210/Ra-226)(o) and SO2 emission rate requires further testing but may have implications for future eruptions. (C) 2004 Elsevier B.V. All rights reserved.

A cross-calibration of chlorine isotopic measurements and suitability of seawater as the international reference material

A collection of 24 seawaters from various worldwide locations and differing depth was culled to measure their chlorine isotopic composition (delta(37)Cl). These samples cover all the oceans and large seas: Atlantic, Pacific, Indian and Antarctic oceans, Mediterranean and Red seas. This collection includes nine seawaters from three depth profiles down to 4560 mbsl. The standard deviation (2sigma) of the delta(37)Cl of this collection is +/-0.08 parts per thousand, which is in fact as large as our precision of measurement ( +/- 0.10 parts per thousand). Thus, within error, oceanic waters seem to be an homogeneous reservoir. According to our results, any seawater could be representative of Standard Mean Ocean Chloride (SMOC) and could be used as a reference standard. An extended international cross-calibration over a large range of delta(37)Cl has been completed. For this purpose, geological fluid samples of various chemical compositions and a manufactured CH3Cl gas sample, with delta(37)Cl from about -6 parts per thousand to +6 parts per thousand have been compared. Data were collected by gas source isotope ratio mass spectrometry (IRMS) at the Paris, Reading and Utrecht laboratories and by thermal ionization mass spectrometry (TIMS) at the Leeds laboratory. Comparison of IRMS values over the range -5.3 parts per thousand to +1.4 parts per thousand plots on the Y=X line, showing a very good agreement between the three laboratories. On 11 samples, the trend line between Paris and Reading Universities is: delta(37)Cl(Reading)= (1.007 +/- 0.009)delta(37)Cl(Paris) - (0.040 +/- 0.025), with a correlation coefficient: R-2 = 0.999. TIMS values from Leeds University have been compared to IRMS values from Paris University over the range -3.0 parts per thousand to +6.0 parts per thousand. On six samples, the agreement between these two laboratories, using different techniques is good: delta(37)Cl(Leeds)=(1.052 +/- 0.038)delta(37)Cl(Paris) + (0.058 +/- 0.099), with a correlation coefficient: R-2 = 0.995. The present study completes a previous cross-calibration between the Leeds and Reading laboratories to compare TIMS and IRMS results (Anal. Chem. 72 (2000) 2261). Both studies allow a comparison of IRMS and TIMS techniques between delta(37)Cl values from -4.4 parts per thousand to +6.0 parts per thousand and show a good agreement: delta(37)Cl(TIMS)=(1.039 +/- 0.023)delta(37)Cl(IRMS)+(0.059 +/- 0.056), with a correlation coefficient: R-2 = 0.996. Our study shows that, for fluid samples, if chlorine isotopic compositions are near 0 parts per thousand, their measurements either by IRMS or TIMS will give comparable results within less than +/- 0.10 parts per thousand, while for delta(37)Cl values as far as 10 parts per thousand (either positive or negative) from SMOC, both techniques will agree within less than +/- 0.30 parts per thousand. (C) 2004 Elsevier B.V. All rights reserved.

Pb-210-Ra-226 and Ra-228-Th-232 systematics in young arc lavas: implications for magma degassing and ascent rates

New data show that island arc rocks have (Pb-210/Ra-226)(o) ratios which range from as low as 0.24 up to 2.88. In contrast, (Ra-22S/Th-232) appears always within error of I suggesting that the large Ra-226-excesses observed in arc rocks were generated more than 30 years ago. This places a maximum estimate on melt ascent velocities of around 4000 m/year and provides further confidence that the Ra-226 excesses reflect deep (source) processes rather than shallow level alteration or seawater contamination. Conversely, partial melting must have occurred more than 30 years prior to eruption. The Pb-210 deficits are most readily explained by protracted magma degassing. Using published numerical models, the data suggest that degassing occurred continuously for periods up to several decades just prior to eruption but no link with eruption periodicity was found. Longer periods are required if degassing is discontinuous, less than 100% efficient or if magma is recharged or stored after degassing. The long durations suggest much of this degassing occurs at depth with implications for the formation of hydrothermal and copper-porphyry systems. A suite of lavas erupted in 1985-1986 from Sangeang Api volcano in the Sunda arc are characterised by deficits of Pb-210 relative to Ra-226 from which 6-8 years of continuous Rn-222 degassing would be inferred from recent numerical models. These data also form a linear (Pb-210)/Pb-(Ra-226)/Pb array which might be interpreted as a 71-year isochron. However, the array passes through the origin suggesting displacement downwards from the equiline in response to degassing and so the slope of the array is inferred not to have any age significance. Simple modelling shows that the range of (Ra-226)/Pb ratios requires thousands of years to develop consistent with differentiation occurring in response to cooling at the base of the crust. Thus, degassing post-dated, and was not responsible for magma differentiation. The formation, migration and extraction of gas bubbles must be extremely efficient in mafic magma whereas the higher viscosity of more siliceous magmas retards the process and can lead to Pb-210 excesses. A possible negative correlation between (Pb-210/Ra-226)(o) and SO2 emission rate requires further testing but may have implications for future eruptions. (C) 2004 Elsevier B.V. All rights reserved.