Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Integration of a 3D Variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay

This paper describes the implementation of a 3D variational (3D-Var) data assimilation scheme for a morphodynamic model applied to Morecambe Bay, UK. A simple decoupled hydrodynamic and sediment transport model is combined with a data assimilation scheme to investigate the ability of such methods to improve the accuracy of the predicted bathymetry. The inverse forecast error covariance matrix is modelled using a Laplacian approximation which is calibrated for the length scale parameter required. Calibration is also performed for the Soulsby-van Rijn sediment transport equations. The data used for assimilation purposes comprises waterlines derived from SAR imagery covering the entire period of the model run, and swath bathymetry data collected by a ship-borne survey for one date towards the end of the model run. A LiDAR survey of the entire bay carried out in November 2005 is used for validation purposes. The comparison of the predictive ability of the model alone with the model-forecast-assimilation system demonstrates that using data assimilation significantly improves the forecast skill. An investigation of the assimilation of the swath bathymetry as well as the waterlines demonstrates that the overall improvement is initially large, but decreases over time as the bathymetry evolves away from that observed by the survey. The result of combining the calibration runs into a pseudo-ensemble provides a higher skill score than for a single optimized model run. A brief comparison of the Optimal Interpolation assimilation method with the 3D-Var method shows that the two schemes give similar results.

Impact of duration thresholds on Atlantic tropical cyclone counts*

Records of Atlantic basin tropical cyclones (TCs) since the late nineteenth century indicate a very large upward trend in storm frequency. This increase in documented TCs has been previously interpreted as resulting from anthropogenic climate change. However, improvements in observing and recording practices provide an alternative interpretation for these changes: recent studies suggest that the number of potentially missed TCs is sufficient to explain a large part of the recorded increase in TC counts. This study explores the influence of another factor—TC duration—on observed changes in TC frequency, using a widely used Atlantic hurricane database (HURDAT). It is found that the occurrence of short-lived storms (duration of 2 days or less) in the database has increased dramatically, from less than one per year in the late nineteenth–early twentieth century to about five per year since about 2000, while medium- to long-lived storms have increased little, if at all. Thus, the previously documented increase in total TC frequency since the late nineteenth century in the database is primarily due to an increase in very short-lived TCs. The authors also undertake a sampling study based upon the distribution of ship observations, which provides quantitative estimates of the frequency of missed TCs, focusing just on the moderate to long-lived systems with durations exceeding 2 days in the raw HURDAT. Upon adding the estimated numbers of missed TCs, the time series of moderate to long-lived Atlantic TCs show substantial multidecadal variability, but neither time series exhibits a significant trend since the late nineteenth century, with a nominal decrease in the adjusted time series. Thus, to understand the source of the century-scale increase in Atlantic TC counts in HURDAT, one must explain the relatively monotonic increase in very short-duration storms since the late nineteenth century. While it is possible that the recorded increase in short-duration TCs represents a real climate signal, the authors consider that it is more plausible that the increase arises primarily from improvements in the quantity and quality of observations, along with enhanced interpretation techniques. These have allowed National Hurricane Center forecasters to better monitor and detect initial TC formation, and thus incorporate increasing numbers of very short-lived systems into the TC database.

Transport impacts on atmosphere and climate: shipping

Emissions of exhaust gases and particles from oceangoing ships are a significant and growing contributor to the total emissions from the transportation sector. We present an assessment of the contribution of gaseous and particulate emissions from oceangoing shipping to anthropogenic emissions and air quality. We also assess the degradation in human health and climate change created by these emissions. Regulating ship emissions requires comprehensive knowledge of current fuel consumption and emissions, understanding of their impact on atmospheric composition and climate, and projections of potential future evolutions and mitigation options. Nearly 70% of ship emissions occur within 400 km of coastlines, causing air quality problems through the formation of ground-level ozone, sulphur emissions and particulate matter in coastal areas and harbours with heavy traffic. Furthermore, ozone and aerosol precursor emissions as well as their derivative species from ships may be transported in the atmosphere over several hundreds of kilometres, and thus contribute to air quality problems further inland, even though they are emitted at sea. In addition, ship emissions impact climate. Recent studies indicate that the cooling due to altered clouds far outweighs the warming effects from greenhouse gases such as carbon dioxide (CO2) or ozone from shipping, overall causing a negative present-day radiative forcing (RF). Current efforts to reduce sulphur and other pollutants from shipping may modify this. However, given the short residence time of sulphate compared to CO2, the climate response from sulphate is of the order decades while that of CO2 is centuries. The climatic trade-off between positive and negative radiative forcing is still a topic of scientific research, but from what is currently known, a simple cancellation of global mean forcing components is potentially inappropriate and a more comprehensive assessment metric is required. The CO2 equivalent emissions using the global temperature change potential (GTP) metric indicate that after 50 years the net global mean effect of current emissions is close to zero through cancellation of warming by CO2 and cooling by sulphate and nitrogen oxides.

Assessing levels of uncertainty in recent temperature time series

We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease.

In optics humidity compensation in NDIR exhaust gas measurements of NO2

NDIR is proposed for monitoring of air pollutants emitted by ship engines. Careful optical filtering overcomes the challenge of optical detection of NO2 in humid exhaust gas, despite spectroscopic overlap with the water vapour band.

Changes in significant and maximum wave heights in the Norwegian Sea

This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. The 30-minute Ship-Borne Wave Recorder measurements of Hmax and Hs are shown to be consistent with theoretical wave distributions. The linear regression between Hmax and Hs has a slope of 1.53. Neither Hs nor Hmax show a significant trend in the period 2000–2009. These data are combined with earlier observations. The long-term trend over the period 1980–2009 in annual Hs is 2.72 ± 0.88 cm/year. Mean Hs and Hmax are both correlated with the North Atlantic Oscillation (NAO) index during winter. The correlation with the NAO index is highest for the more frequently encountered (75th percentile) wave heights. The wave field variability associated with the NAO index is reconstructed using a 500-year NAO index record. Hs and Hmax are found to vary by up to 1.42 m and 3.10 m respectively over the 500-year period. Trends in all 30-year segments of the reconstructed wave field are lower than the trend in the observations during 1980–2009. The NAO index does not change significantly in 21st century projections from CMIP5 climate models under scenario RCP85, and thus no NAO-related changes are expected in the mean and extreme wave fields of the Norwegian Sea.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

In situ observations in cyclones over Fram Strait

During the international FRAMZY expedition in March 2002 in-situ observations of Fram Strait cyclones were made by aircraft, ship and automatic buoys in order to study the interaction between cyclones and sea ice. The atmospheric characteristics of the observed cyclones are presented in this paper. The cyclones were generated in the baroclinic zone at the ice edge and moved NNE-ward along the ice edge. This was supported by warm air advection from WSW by an upper-level wave. The cyclones were rather small (diameter 200– 700 km) and shallow (1–1.5 km e-folding height for the horizontal pressure and temperature difference) with life times between 12 and 36 hours. In spite of the small space and time scales, remarkable extremes were observed within the cyclones. Winds reached maxima above 20 ms−1 lasting for only a few hours. The transition from the cold to the advancing warm air over sea ice occurred within narrow (5–30 km) frontal zones in which vorticity and convergence reached maxima on the order of 10−3 s−1. It is discussed whether the sea ice in spite of its inertia is able to react on these strong sub cyclone-scale processes and, thus, these processes have to be taken into account in models in order to simulate the cyclone-sea ice interaction properly.

Going with the floe

Julia Wilkinson and a Zooniverse citizen-science team examine Arctic auroral data, using observations from the ill-fated 19th-century Arctic exploration ship USS Jeannette.