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.

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.

Response of the North Atlantic wave climate to atmospheric modes of variability

This study investigates the relationship between the wind wave climate and the main climate modes of atmospheric variability in the North Atlantic Ocean. The modes considered are the North Atlantic Oscillation (NAO), the East Atlantic (EA) pattern, the East Atlantic Western Russian (EA/WR) pattern and the Scandinavian (SCAN) pattern. The wave dataset consists of buoys records, remote sensing altimetry observations and a numerical hindcast providing significant wave height (SWH), mean wave period (MWP) and mean wave direction (MWD) for the period 1989–2009. After evaluating the reliability of the hindcast, we focus on the impact of each mode on seasonal wave parameters and on the relative importance of wind-sea and swell components. Results demonstrate that the NAO and EA patterns are the most relevant, whereas EA/WR and SCAN patterns have a weaker impact on the North Atlantic wave climate variability. During their positive phases, both NAO and EA patterns are related to winter SWH at a rate that reaches 1 m per unit index along the Scottish coast (NAO) and Iberian coast (EA) patterns. In terms of winter MWD, the two modes induce a counterclockwise shift of up to 65° per negative NAO (positive EA) unit over west European coasts. They also increase the winter MWP in the North Sea and in the Bay of Biscay (up to 1 s per unit NAO) and along the western coasts of Europe and North Africa (1 s per unit EA). The impact of winter EA pattern on all wave parameters is mostly caused through the swell wave component.

On the ability of statistical wind-wave models to capture the variability and long-term trends of the North Atlantic winter wave climate

A dynamical wind-wave climate simulation covering the North Atlantic Ocean and spanning the whole 21st century under the A1B scenario has been compared with a set of statistical projections using atmospheric variables or large scale climate indices as predictors. As a first step, the performance of all statistical models has been evaluated for the present-day climate; namely they have been compared with a dynamical wind-wave hindcast in terms of winter Significant Wave Height (SWH) trends and variance as well as with altimetry data. For the projections, it has been found that statistical models that use wind speed as independent variable predictor are able to capture a larger fraction of the winter SWH inter-annual variability (68% on average) and of the long term changes projected by the dynamical simulation. Conversely, regression models using climate indices, sea level pressure and/or pressure gradient as predictors, account for a smaller SWH variance (from 2.8% to 33%) and do not reproduce the dynamically projected long term trends over the North Atlantic. Investigating the wind-sea and swell components separately, we have found that the combination of two regression models, one for wind-sea waves and another one for the swell component, can improve significantly the wave field projections obtained from single regression models over the North Atlantic.

Projection of global wave climate change towards the end of the 21st century

Wind generated waves at the sea surface are of outstanding importance for both their practical relevance in many aspects, such as coastal erosion, protection, or safety of navigation, and for their scientific relevance in modifying fluxes at the air-sea interface. So far long-term changes in ocean wave climate have been studied mostly from a regional perspective with global dynamical studies emerging only recently. Here a global wave climate study is presented, in which a global wave model (WAM) is driven by atmospheric forcing from a global climate model (ECHAM5) for present day and potential future climate conditions represented by the IPCC (Intergovernmental Panel for Climate Change) A1B emission scenario. It is found that changes in mean and extreme wave climate towards the end of the twenty-first century are small to moderate, with the largest signals being a poleward shift in the annual mean and extreme significant wave heights in the mid-latitudes of both hemispheres, more pronounced in the Southern Hemisphere, and most likely associated with a corresponding shift in mid-latitude storm tracks. These changes are broadly consistent with results from the few studies available so far. The projected changes in the mean wave periods, associated with the changes in the wave climate in the mid to high latitudes, are also shown, revealing a moderate increase in the equatorial eastern side of the ocean basins. This study presents a step forward towards a larger ensemble of global wave climate projections required to better assess robustness and uncertainty of potential future wave climate change.

Sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization

The Canadian Middle Atmosphere Model is used to examine the sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization. Momentum conservation requires that the parameterized gravity wave momentum flux at the top of the model be zero and corresponds to the physical boundary condition of no momentum flux at the top of the atmosphere. Allowing momentum flux to escape the model domain violates momentum conservation. Here the impact of momentum conservation in two sets of model simulations is investigated. In the first set, the simulation of present-day climate for two model-lid height configurations, 0.001 and 10 hPa, which are identical below 10 hPa, is considered. The impact of momentum conservation on the climate with the model lid at 0.001 hPa is minimal, which is expected because of the small amount of gravity wave momentum flux reaching 0.001 hPa. When the lid is lowered to 10 hPa and momentum is conserved, there is only a modest impact on the climate in the Northern Hemisphere; however, the Southern Hemisphere climate is more adversely affected by the deflection of resolved waves near the model lid. When momentum is not conserved in the 10-hPa model the climate is further degraded in both hemispheres, particularly in winter at high latitudes, and the impact of momentum conservation extends all the way to the surface. In the second set of simulations, the impact of momentum conservation and model-lid height on the modeled response to ozone depletion in the Southern Hemisphere is considered, and it is found that the response can display significant sensitivity to both factors. In particular, both the lower-stratospheric polar temperature and surface responses are significantly altered when the lid is lowered, with the effect being most severe when momentum is not conserved. The implications with regard to the current round of Intergovernmental Panel on Climate Change model projections are discussed.

The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0wave propagation mechanism and the CRW interaction. The behaviour of the Charney modes and the first neutral branch, which rely on tropospheric PV gradients, are arguably more applicable to the atmosphere than modes of the Eady model where the positive PV gradient exists only at the tropopause

The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

African easterly wave variability and its relationship to Atlantic tropical cyclone activity

Automatic tracking of vorticity centers in European Centre for Medium-Range Weather Forecasts analyses has been used to develop a 20-yr climatology of African easterly wave activity. The tracking statistics at 600 and 850 mb confirm the complicated easterly wave structures present over the African continent. The rainy zone equatorward of 15 degreesN is dominated by 600-mb activity, and the much drier Saharan region poleward of 15 degreesN is more dominated by 850-mb activity. Over the Atlantic Ocean there is just one storm track with the 600- and 850-mb wave activity collocated. Based on growth/decay and genesis statistics, it appears that the 850-mb waves poleward of 15 degreesN over land generally do not get involved with the equatorward storm track over the ocean. Instead, there appears to be significant development of 850-mb activity at the West African coast in the rainy zone around (10 degreesN, 10 degreesW), which, it is proposed, is associated with latent heat release. Based on the tracking statistics, it has been shown that there is marked interannual variability in African easterly wave (AEW) activity. It is especially marked at the 850-mb level at the West African coast between about 10 degrees and 15 degreesN, where the coefficient of variation is 0.29. For the period between 1985 and 1998, a notable positive correlation is seen between this AEW activity and Atlantic tropical cyclone activity. This correlation is particularly strong for the postreanalysis period between 1994 and 1998. This result suggests that Atlantic tropical cyclone activity may be influenced by the number of AEWs leaving the West African coast, which have significant low-level amplitudes, and not simply by the total number of AEWs.

Convectively coupled equatorial waves: A new methodology for identifying wave structures in observational data

Convectively coupled equatorial waves are fundamental components of the interaction between the physics and dynamics of the tropical atmosphere. A new methodology, which isolates individual equatorial wave modes, has been developed and applied to observational data. The methodology assumes that the horizontal structures given by equatorial wave theory can be used to project upper- and lower-tropospheric data onto equatorial wave modes. The dynamical fields are first separated into eastward- and westward-moving components with a specified domain of frequency–zonal wavenumber. Each of the components for each field is then projected onto the different equatorial modes using the y structures of these modes given by the theory. The latitudinal scale yo of the modes is predetermined by data to fit the equatorial trapping in a suitable latitude belt y = ±Y. The extent to which the different dynamical fields are consistent with one another in their depiction of each equatorial wave structure determines the confidence in the reality of that structure. Comparison of the analyzed modes with the eastward- and westward-moving components in the convection field enables the identification of the dynamical structure and nature of convectively coupled equatorial waves. In a case study, the methodology is applied to two independent data sources, ECMWF Reanalysis and satellite-observed window brightness temperature (Tb) data for the summer of 1992. Various convectively coupled equatorial Kelvin, mixed Rossby–gravity, and Rossby waves have been detected. The results indicate a robust consistency between the two independent data sources. Different vertical structures for different wave modes and a significant Doppler shifting effect of the background zonal winds on wave structures are found and discussed. It is found that in addition to low-level convergence, anomalous fluxes induced by strong equatorial zonal winds associated with equatorial waves are important for inducing equatorial convection. There is evidence that equatorial convection associated with Rossby waves leads to a change in structure involving a horizontal structure similar to that of a Kelvin wave moving westward with it. The vertical structure may also be radically changed. The analysis method should make a very powerful diagnostic tool for investigating convectively coupled equatorial waves and the interaction of equatorial dynamics and physics in the real atmosphere. The results from application of the analysis method for a reanalysis dataset should provide a benchmark against which model studies can be compared.

Unimodality of wave amplitude in the northern Hemisphere

A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960-2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality. The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960-70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude. As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.

Tropospheric planetary wave dynamics and mixture modeling: Two preferred regimes and a regime shift

Investigation of preferred structures of planetary wave dynamics is addressed using multivariate Gaussian mixture models. The number of components in the mixture is obtained using order statistics of the mixing proportions, hence avoiding previous difficulties related to sample sizes and independence issues. The method is first applied to a few low-order stochastic dynamical systems and data from a general circulation model. The method is next applied to winter daily 500-hPa heights from 1949 to 2003 over the Northern Hemisphere. A spatial clustering algorithm is first applied to the leading two principal components (PCs) and shows significant clustering. The clustering is particularly robust for the first half of the record and less for the second half. The mixture model is then used to identify the clusters. Two highly significant extratropical planetary-scale preferred structures are obtained within the first two to four EOF state space. The first pattern shows a Pacific-North American (PNA) pattern and a negative North Atlantic Oscillation (NAO), and the second pattern is nearly opposite to the first one. It is also observed that some subspaces show multivariate Gaussianity, compatible with linearity, whereas others show multivariate non-Gaussianity. The same analysis is also applied to two subperiods, before and after 1978, and shows a similar regime behavior, with a slight stronger support for the first subperiod. In addition a significant regime shift is also observed between the two periods as well as a change in the shape of the distribution. The patterns associated with the regime shifts reflect essentially a PNA pattern and an NAO pattern consistent with the observed global warming effect on climate and the observed shift in sea surface temperature around the mid-1970s.

An estimate of the global impact of multiple scattering by clouds on outgoing long-wave radiation

Although the potential importance of scattering of long-wave radiation by clouds has been recognised, most studies have concentrated on the impact of high clouds and few estimates of the global impact of scattering have been presented. This study shows that scattering in low clouds has a significant impact on outgoing long-wave radiation (OLR) in regions of marine stratocumulus (-3.5 W m(-2) for overcast conditions) where the column water vapour is relatively low. This corresponds to an enhancement of the greenhouse effect of such clouds by 10%. The near-global impact of scattering on OLR is estimated to be -3.0 W m(-2), with low clouds contributing -0.9 W m(-2), mid-level cloud -0.7 W m(-2) and high clouds -1.4 W m(-2). Although this effect appears small compared to the global mean OLR of 240 W m(-2), it indicates that neglect of scattering will lead to an error in cloud long-wave forcing of about 10% and an error in net cloud forcing of about 20%.

Observed and simulated precursors of stratospheric polar vortex anomalies in the Northern Hemisphere

The Northern Hemisphere stratospheric polar vortex is linked to surface weather. After Stratospheric Sudden Warmings in winter, the tropospheric circulation is often nudged towards the negative phase of the Northern Annular Mode (NAM) and the North Atlantic Oscillation (NAO). A strong stratospheric vortex is often associated with subsequent positive NAM/NAO conditions. For stratosphere–troposphere associations to be useful for forecasting purposes it is crucial that changes to the stratospheric vortex can be understood and predicted. Recent studies have proposed that there exist tropospheric precursors to anomalous vortex events in the stratosphere and that these precursors may be understood by considering the relationship between stationary wave patterns and regional variability. Another important factor is the extent to which the inherent variability of the stratosphere in an atmospheric model influences its ability to simulate stratosphere–troposphere links. Here we examine the lower stratosphere variability in 300-year pre-industrial control integrations from 13 coupled climate models. We show that robust precursors to stratospheric polar vortex anomalies are evident across the multi-model ensemble. The most significant tropospheric component of these precursors consists of a height anomaly dipole across northern Eurasia and large anomalies in upward stationary wave fluxes in the lower stratosphere over the continent. The strength of the stratospheric variability in the models was found to depend on the variability of the upward stationary wave fluxes and the amplitude of the stationary waves.

Reduced height (Rht) and photoperiod insensitivity (Ppd) allele associations with establishment and early growth of wheat in contrasting production systems

Near isogenic lines (NILs) varying for genes for reduced height (Rht) and photoperiod insensitivity (Ppd-D1a) in a cv. Mercia background (rht (tall), Rht-B1b, Rht-D1b, Rht-B1c, Rht8c + Ppd-D1a, Rht-D1c, Rht12) were compared at one field site but within contrasting ('organic' vs. 'conventional') rotational and agronomic contexts, in each of 3 years. In the final year, further NILs (rht (tall), Rht-B1b, Rht-D1b, Rht-B1c, Rht-B1b + Rht-D1b, Rht-D1b + Rht-B1c) in both Maris Huntsman and Maris Widgeon backgrounds were added together with 64 lines of a doubled haploid (DH) population [Savannah (Rht-D1b) x Renesansa (Rht-8c + Ppd-D1a)]. Assessments included laboratory tests of germination and coleoptile length, and various field measurements of crop growth between emergence and pre jointing [plant population, tillering, leaf length, ground cover (GC), interception of photosynthetically active radiation (PAR), crop dry matter (DM) and nitrogen accumulation (N), far red: red reflectance ratio (FR:R), crop height, and weed dry matter]. All of the dwarfing alleles except Rht12 in the Mercia background and Rht8c in the DHs were associated with reduced coleoptile length. Most of the dwarfing alleles (depending on background) reduced seed viability. Severe dwarfing alleles (Rht-B1c, Rht-D1c and Rht12) were routinely associated with fewer plant numbers and reduced early crop growth (GC, PAR, DM, N, FR:R), and in 1 year, increased weed DM. In the Mercia background and the DHs the semi-dwarfing allele Rht-D1b was also sometimes associated with reductions in early crop growth; no such negative effects were associated with the marker for Rht8c. When significant interactions between cropping system and genotype did occur it was because differences between lines were more exaggerated in the organic system than in the conventional system. Ppd-D1a was associated positively with plant numbers surviving the winter and early crop growth (GC, FR:R, DM, N, PAR, height), and was the most significant locus in a QTL analysis. We conclude that, within these environmental and system contexts, genes moderating development are likely to be more important in influencing early resource capture than using Rht8c as an alternative semi-dwarfing gene to Rht-D1b.