An optimal inverse method using Doppler lidar measurements to estimate the surface sensible heat flux

Inverse methods are widely used in various fields of atmospheric science. However, such methods are not commonly used within the boundary-layer community, where robust observations of surface fluxes are a particular concern. We present a new technique for deriving surface sensible heat fluxes from boundary-layer turbulence observations using an inverse method. Doppler lidar observations of vertical velocity variance are combined with two well-known mixed-layer scaling forward models for a convective boundary layer (CBL). The inverse method is validated using large-eddy simulations of a CBL with increasing wind speed. The majority of the estimated heat fluxes agree within error with the proscribed heat flux, across all wind speeds tested. The method is then applied to Doppler lidar data from the Chilbolton Observatory, UK. Heat fluxes are compared with those from a mast-mounted sonic anemometer. Errors in estimated heat fluxes are on average 18 %, an improvement on previous techniques. However, a significant negative bias is observed (on average −63%) that is more pronounced in the morning. Results are improved for the fully-developed CBL later in the day, which suggests that the bias is largely related to the choice of forward model, which is kept deliberately simple for this study. Overall, the inverse method provided reasonable flux estimates for the simple case of a CBL. Results shown here demonstrate that this method has promise in utilizing ground-based remote sensing to derive surface fluxes. Extension of the method is relatively straight-forward, and could include more complex forward models, or other measurements.

Large-scale dynamics associated with clustering of extratropical cyclones affecting Western Europe

Some recent winters in Western Europe have been characterized by the occurrence of multiple extratropical cyclones following a similar path. The occurrence of such cyclone clusters leads to large socio-economic impacts due to damaging winds, storm surges, and floods. Recent studies have statistically characterized the clustering of extratropical cyclones over the North Atlantic and Europe and hypothesized potential physical mechanisms responsible for their formation. Here we analyze 4 months characterized by multiple cyclones over Western Europe (February 1990, January 1993, December 1999, and January 2007). The evolution of the eddy driven jet stream, Rossby wave-breaking, and upstream/downstream cyclone development are investigated to infer the role of the large-scale flow and to determine if clustered cyclones are related to each other. Results suggest that optimal conditions for the occurrence of cyclone clusters are provided by a recurrent extension of an intensified eddy driven jet toward Western Europe lasting at least 1 week. Multiple Rossby wave-breaking occurrences on both the poleward and equatorward flanks of the jet contribute to the development of these anomalous large-scale conditions. The analysis of the daily weather charts reveals that upstream cyclone development (secondary cyclogenesis, where new cyclones are generated on the trailing fronts of mature cyclones) is strongly related to cyclone clustering, with multiple cyclones developing on a single jet streak. The present analysis permits a deeper understanding of the physical reasons leading to the occurrence of cyclone families over the North Atlantic, enabling a better estimation of the associated cumulative risk over Europe.

Satellite-supported flood forecasting in river networks: a real case study

Satellite-based (e.g., Synthetic Aperture Radar [SAR]) water level observations (WLOs) of the floodplain can be sequentially assimilated into a hydrodynamic model to decrease forecast uncertainty. This has the potential to keep the forecast on track, so providing an Earth Observation (EO) based flood forecast system. However, the operational applicability of such a system for floods developed over river networks requires further testing. One of the promising techniques for assimilation in this field is the family of ensemble Kalman (EnKF) filters. These filters use a limited-size ensemble representation of the forecast error covariance matrix. This representation tends to develop spurious correlations as the forecast-assimilation cycle proceeds, which is a further complication for dealing with floods in either urban areas or river junctions in rural environments. Here we evaluate the assimilation of WLOs obtained from a sequence of real SAR overpasses (the X-band COSMO-Skymed constellation) in a case study. We show that a direct application of a global Ensemble Transform Kalman Filter (ETKF) suffers from filter divergence caused by spurious correlations. However, a spatially-based filter localization provides a substantial moderation in the development of the forecast error covariance matrix, directly improving the forecast and also making it possible to further benefit from a simultaneous online inflow error estimation and correction. Additionally, we propose and evaluate a novel along-network metric for filter localization, which is physically-meaningful for the flood over a network problem. Using this metric, we further evaluate the simultaneous estimation of channel friction and spatially-variable channel bathymetry, for which the filter seems able to converge simultaneously to sensible values. Results also indicate that friction is a second order effect in flood inundation models applied to gradually varied flow in large rivers. The study is not conclusive regarding whether in an operational situation the simultaneous estimation of friction and bathymetry helps the current forecast. Overall, the results indicate the feasibility of stand-alone EO-based operational flood forecasting.

The dynamics of Baroclinic Zonal jets

Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

Note: A balloon-borne accelerometer technique for measuring atmospheric turbulence

A weather balloon and its suspended instrument package behave like a pendulum with a moving pivot. This dynamical system is exploited here for the detection of atmospheric turbulence. By adding an accelerometer to the instrument package, the size of the swings induced by atmospheric turbulence can be measured. In test flights, strong turbulence has induced accelerations greater than 5g, where g = 9.81 m s−2. Calibration of the accelerometer data with a vertically orientated lidar has allowed eddy dissipation rate values of between 10−3 and 10−2 m2 s−3 to be derived from the accelerometer data. The novel use of a whole weather balloon and its adapted instrument package can be used as a new instrument to make standardized in situ measurements of turbulence.

Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing nonlinearity

We systematically compare the performance of ETKF-4DVAR, 4DVAR-BEN and 4DENVAR with respect to two traditional methods (4DVAR and ETKF) and an ensemble transform Kalman smoother (ETKS) on the Lorenz 1963 model. We specifically investigated this performance with increasing nonlinearity and using a quasi-static variational assimilation algorithm as a comparison. Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering (1) assimilation window length and observation interval size and (2) ensemble size to investigate the influence of hybrid background error covariance matrices and nonlinearity on the performance of the methods. For short assimilation windows with close to linear dynamics, it has been shown that all hybrid methods show an improvement in RMSE compared to the traditional methods. For long assimilation window lengths in which nonlinear dynamics are substantial, the variational framework can have diffculties fnding the global minimum of the cost function, so we explore a quasi-static variational assimilation (QSVA) framework. Of the hybrid methods, it is seen that under certain parameters, hybrid methods which do not use a climatological background error covariance do not need QSVA to perform accurately. Generally, results show that the ETKS and hybrid methods that do not use a climatological background error covariance matrix with QSVA outperform all other methods due to the full flow dependency of the background error covariance matrix which also allows for the most nonlinearity.

The slowly evolving background state of the atmosphere

The theory of wave–mean flow interaction requires a partition of the atmospheric flow into a notional background state and perturbations to it. Here, a background state, known as the Modified Lagrangian Mean (MLM), is defined as the zonally symmetric state obtained by requiring that every potential vorticity (PV) contour lying within an isentropic layer encloses the same mass and circulation as in the full flow. For adiabatic and frictionless flow, these two integral properties are time-invariant and the MLM state is a steady solution of the primitive equations. The time dependence in the adiabatic flow is put into the perturbations, which can be described by a wave-activity conservation law that is exact even at large amplitude. Furthermore, the effects of non-conservative processes on wave activity can be calculated from the conservation law. A new method to calculate the MLM state is introduced, where the position of the lower boundary is obtained as part of the solution. The results are illustrated using Northern Hemisphere ERA-Interim data. The MLM state evolves slowly, implying that the net non-conservative effects are weak. Although ‘adiabatic eddy fluxes’ cannot affect the MLM state, the effects of Rossby-wave breaking, PV filamentation and subsequent dissipation result in sharpening of the polar vortex edge and meridional shifts in the MLM zonal flow, both at tropopause level and on the winter stratospheric vortex. The rate of downward migration of wave activity during stratospheric sudden warmings is shown to be given by the vertical scale associated with polar vortex tilt divided by the time-scale for wave dissipation estimated from the wave-activity conservation law. Aspects of troposphere–stratosphere interaction are discussed. The new framework is suitable to examine the climate and its interactions with disturbances, such as midlatitude storm tracks, and makes a clean partition between adiabatic and non-conservative processes.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

How is the balance of a forecast ensemble affected by adaptive and non-adaptive localization schemes?

This paper investigates the effect on balance of a number of Schur product-type localization schemes which have been designed with the primary function of reducing spurious far-field correlations in forecast error statistics. The localization schemes studied comprise a non-adaptive scheme (where the moderation matrix is decomposed in a spectral basis), and two adaptive schemes, namely a simplified version of SENCORP (Smoothed ENsemble COrrelations Raised to a Power) and ECO-RAP (Ensemble COrrelations Raised to A Power). The paper shows, we believe for the first time, how the degree of balance (geostrophic and hydrostatic) implied by the error covariance matrices localized by these schemes can be diagnosed. Here it is considered that an effective localization scheme is one that reduces spurious correlations adequately but also minimizes disruption of balance (where the 'correct' degree of balance or imbalance is assumed to be possessed by the unlocalized ensemble). By varying free parameters that describe each scheme (e.g. the degree of truncation in the schemes that use the spectral basis, the 'order' of each scheme, and the degree of ensemble smoothing), it is found that a particular configuration of the ECO-RAP scheme is best suited to the convective-scale system studied. According to our diagnostics this ECO-RAP configuration still weakens geostrophic and hydrostatic balance, but overall this is less so than for other schemes.

Possible impacts of a future grand solar minimum on climate: stratospheric and global circulation changes

It has been suggested that the Sun may evolve into a period of lower activity over the 21st century. This study examines the potential climate impacts of the onset of an extreme ‘Maunder Minimum like’ grand solar minimum using a comprehensive global climate model. Over the second half of the 21st century, the scenario assumes a decrease in total solar irradiance of 0.12% compared to a reference RCP8.5 experiment. The decrease in solar irradiance cools the stratopause (~1 hPa) in the annual and global mean by 1.4 K. The impact on global mean near-surface temperature is small (~−0.1 K), but larger changes in regional climate occur during the stratospheric dynamically active seasons. In Northern hemisphere (NH) winter-time, there is a weakening of the stratospheric westerly jet by up to ~3-4 m s1, with the largest changes occurring in January-February. This is accompanied by a deepening of the Aleutian low at the surface and an increase in blocking over northern Europe and the north Pacific. There is also an equatorward shift in the Southern hemisphere (SH) midlatitude eddy-driven jet in austral spring. The occurrence of an amplified regional response during winter and spring suggests a contribution from a top-down pathway for solar-climate coupling; this is tested using an experiment in which ultraviolet (200–320 nm) radiation is decreased in isolation of other changes. The results show that a large decline in solar activity over the 21st century could have important impacts on the stratosphere and regional surface climate.

Joint retrievals of cloud and drizzle in marine boundary layer clouds using ground-based radar, lidar and zenith radiances

Active remote sensing of marine boundary-layer clouds is challenging as drizzle drops often dominate the observed radar reflectivity. We present a new method to simultaneously retrieve cloud and drizzle vertical profiles in drizzling boundary-layer clouds using surface-based observations of radar reflectivity, lidar attenuated backscatter, and zenith radiances under conditions when precipitation does not reach the surface. Specifically, the vertical structure of droplet size and water content of both cloud and drizzle is characterised throughout the cloud. An ensemble optimal estimation approach provides full error statistics given the uncertainty in the observations. To evaluate the new method, we first perform retrievals using synthetic measurements from large-eddy simulation snapshots of cumulus under stratocumulus, where cloud water path is retrieved with an error of 31 g m−2 . The method also performs well in non-drizzling clouds where no assumption of the cloud profile is required. We then apply the method to observations of marine stratocumulus obtained during the Atmospheric Radiation Measurement MAGIC deployment in the Northeast Pacific. Here, retrieved cloud water path agrees well with independent three-channel microwave radiometer retrievals, with a root mean square difference of 10–20 g m−2.

Separating the influence of projected changes in air temperature and wind on patterns of sea level change and ocean heat content

We present ocean model sensitivity experiments aimed at separating the influence of the projected changes in the “thermal” (near-surface air temperature) and “wind” (near-surface winds) forcing on the patterns of sea level and ocean heat content. In the North Atlantic, the distribution of sea level change is more due to the “thermal” forcing, whereas it is more due to the “wind” forcing in the North Pacific; in the Southern Ocean, the “thermal” and “wind” forcing have a comparable influence. In the ocean adjacent to Antarctica the “thermal” forcing leads to an inflow of warmer waters on the continental shelves, which is somewhat attenuated by the “wind” forcing. The structure of the vertically integrated heat uptake is set by different processes at low and high latitudes: at low latitudes it is dominated by the heat transport convergence, whereas at high latitudes it represents a small residual of changes in the surface flux and advection of heat. The structure of the horizontally integrated heat content tendency is set by the increase of downward heat flux by the mean circulation and comparable decrease of upward heat flux by the subgrid-scale processes; the upward eddy heat flux decreases and increases by almost the same magnitude in response to, respectively, the “thermal” and “wind” forcing. Regionally, the surface heat loss and deep convection weaken in the Labrador Sea, but intensify in the Greenland Sea in the region of sea ice retreat. The enhanced heat flux anomaly in the subpolar Atlantic is mainly caused by the “thermal” forcing.

The solsticial pause on Mars: 2 modelling and investigation of causes

The martian solsticial pause, presented in a companion paper (Lewis et al., this issue), was investigated further through a series of model runs using the UK version of the LMD/UK Mars Global Climate Model. It was found that the pause could not be adequately reproduced if radiatively active water ice clouds were omitted from the model. When clouds were used, along with a realistic time-dependent dust opacity distribution, a substantial minimum in near-surface transient eddy activity formed around solstice in both hemispheres. The net effect of the clouds in the model is, by altering the thermal structure of the atmosphere, to decrease the vertical shear of the westerly jet near the surface around solstice, and thus reduce baroclinic growth rates. A similar effect was seen under conditions of large dust loading, implying that northern midlatitude eddy activity will tend to become suppressed after a period of intense flushing storm formation around the northern cap edge. Suppression of baroclinic eddy generation by the barotropic component of the flow and via diabatic eddy dissipation were also investigated as possible mechanisms leading to the formation of the solsticial pause but were found not to make major contributions. Zonal variations in topography were found to be important, as their presence results in weakened transient eddies around winter solstice in both hemispheres, through modification of the near-surface flow. The zonal topographic asymmetry appears to be the primary reason for the weakness of eddy activity in the southern hemisphere relative to the northern hemisphere, and the ultimate cause of the solsticial pause in both hemispheres. The meridional topographic gradient was found to exert a much weaker influence on near-surface transient eddies.

Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics

To improve the quantity and impact of observations used in data assimilation it is necessary to take into account the full, potentially correlated, observation error statistics. A number of methods for estimating correlated observation errors exist, but a popular method is a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. The accuracy of the results it yields is unknown as the diagnostic is sensitive to the difference between the exact background and exact observation error covariances and those that are chosen for use within the assimilation. It has often been stated in the literature that the results using this diagnostic are only valid when the background and observation error correlation length scales are well separated. Here we develop new theory relating to the diagnostic. For observations on a 1D periodic domain we are able to the show the effect of changes in the assumed error statistics used in the assimilation on the estimated observation error covariance matrix. We also provide bounds for the estimated observation error variance and eigenvalues of the estimated observation error correlation matrix. We demonstrate that it is still possible to obtain useful results from the diagnostic when the background and observation error length scales are similar. In general, our results suggest that when correlated observation errors are treated as uncorrelated in the assimilation, the diagnostic will underestimate the correlation length scale. We support our theoretical results with simple illustrative examples. These results have potential use for interpreting the derived covariances estimated using an operational system.

Spatial and temporal variations of the seasonal sea level cycle in the northwest Pacific

The seasonal sea level variations observed from tide gauges over 1900-2013 and gridded satellite altimeter product AVISO over 1993-2013 in the northwest Pacific have been explored. The seasonal cycle is able to explain 60-90% of monthly sea level variance in the marginal seas, while it explains less than 20% of variance in the eddy-rich regions. The maximum annual and semi-annual sea level cycles (30cm and 6cm) are observed in the north of the East China Sea and the west of the South China Sea respectively. AVISO was found to underestimate the annual amplitude by 25% compared to tide gauge estimates along the coasts of China and Russia. The forcing for the seasonal sea level cycle was identified. The atmospheric pressure and the steric height produce 8-12cm of the annual cycle in the middle continental shelf and in the Kuroshio Current regions separately. The removal of the two attributors from total sea level permits to identify the sea level residuals that still show significant seasonality in the marginal seas. Both nearby wind stress and surface currents can explain well the long-term variability of the seasonal sea level cycle in the marginal seas and the tropics because of their influence on the sea level residuals. Interestingly, the surface currents are a better descriptor in the areas where the ocean currents are known to be strong. Here, they explain 50-90% of inter-annual variability due to the strong links between the steric height and the large-scale ocean currents.