Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Sea-breeze dynamics and convection initiation: the influence of convective parameterization in weather and climate model biases

There are some long-established biases in atmospheric models that originate from the representation of tropical convection. Previously, it has been difficult to separate cause and effect because errors are often the result of a number of interacting biases. Recently, researchers have gained the ability to run multiyear global climate model simulations with grid spacings small enough to switch the convective parameterization off, which permits the convection to develop explicitly. There are clear improvements to the initiation of convective storms and the diurnal cycle of rainfall in the convection-permitting simulations, which enables a new process-study approach to model bias identification. In this study, multiyear global atmosphere-only climate simulations with and without convective parameterization are undertaken with the Met Office Unified Model and are analyzed over the Maritime Continent region, where convergence from sea-breeze circulations is key for convection initiation. The analysis shows that, although the simulation with parameterized convection is able to reproduce the key rain-forming sea-breeze circulation, the parameterization is not able to respond realistically to the circulation. A feedback of errors also occurs: the convective parameterization causes rain to fall in the early morning, which cools and wets the boundary layer, reducing the land–sea temperature contrast and weakening the sea breeze. This is, however, an effect of the convective bias, rather than a cause of it. Improvements to how and when convection schemes trigger convection will improve both the timing and location of tropical rainfall and representation of sea-breeze circulations.

Piriformospora indica reduces Fusarium head blight disease severity and mycotoxin DON contamination in wheat under UK weather conditions

Piriformospora indica (Sebacinaceae) is a cultivable root endophytic fungus. It colonises the roots of a wide range of host plants. In many settings colonisation promotes host growth, increases yield and protects the host from fungal diseases. We evaluated the effect of P. indica on Fusarium head blight (FHB) disease of winter (cv. Battalion) and spring (cv. Paragon, Mulika, Zircon, Granary, KWS Willow and KWS Kilburn) wheat and consequent contamination by the mycotoxin deoxynivalenol (DON) under UK weather conditions. Interactions of P. indica with an arbuscular mycorrhizal fungus (Funneliformis mosseae), fungicide application (Aviator Xpro) and low and high fertiliser levels were considered. P. indica application reduced FHB disease severity and incidence by 70%. It decreased mycotoxin DON concentration of winter and spring wheat samples by 70% and 80% respectively. P. indica also increased above ground biomass, 1000 grain weight and total grain weight. P. indica reduced disease severity and increased yield in both high and low fertiliser levels. The effect of P. indica was compatible with F. mosseae and foliar fungicide application. P. indica did not have any effects on plant tissue nutrients. These results suggest that P. indica might be useful in biological control of Fusarium diseases of wheat.

Lightning as a space-weather hazard: UK thunderstorm activity modulated by the passage of the heliospheric current sheet

Lightning flash rates, RL, are modulated by corotating interaction regions (CIRs) and the polarity of the heliospheric magnetic field (HMF) in near-Earth space. As the HMF polarity reverses at the heliospheric current sheet (HCS), typically within a CIR, these phenomena are likely related. In this study, RL is found to be significantly enhanced at the HCS and at 27 days prior/after. The strength of the enhancement depends on the polarity of the HMF reversal at the HCS. Near-Earth solar and galactic energetic particle fluxes are also ordered by HMF polarity, though the variations qualitatively differ from RL, with the main increase occurring prior to the HCS crossing. Thus, the CIR effect on lightning is either the result of compression/amplification of the HMF (and its subsequent interaction with the terrestrial system) or that energetic particle preconditioning of the Earth system prior to the HMF polarity change is central to solar wind lightning coupling mechanism.

The impact of a thermodynamic sea-ice module in the COSMO numerical weather prediction model on simulations for the Laptev Sea, Siberian Arctic

Previous versions of the Consortium for Small-scale Modelling (COSMO) numerical weather prediction model have used a constant sea-ice surface temperature, but observations show a high degree of variability on sub-daily timescales. To account for this, we have implemented a thermodynamic sea-ice module in COSMO and performed simulations at a resolution of 15 km and 5 km for the Laptev Sea area in April 2008. Temporal and spatial variability of surface and 2-m air temperature are verified by four automatic weather stations deployed along the edge of the western New Siberian polynya during the Transdrift XIII-2 expedition and by surface temperature charts derived from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite data. A remarkable agreement between the new model results and these observations demonstrates that the implemented sea-ice module can be applied for short-range simulations. Prescribing the polynya areas daily, our COSMO simulations provide a high-resolution and high-quality atmospheric data set for the Laptev Sea for the period 14-30 April 2008. Based on this data set, we derive a mean total sea-ice production rate of 0.53 km3/day for all Laptev Sea polynyas under the assumption that the polynyas are ice-free and a rate of 0.30 km3/day if a 10-cm-thin ice layer is assumed. Our results indicate that ice production in Laptev Sea polynyas has been overestimated in previous studies.

Coordinated weather balloon solar radiation measurements during a solar eclipse

Solar eclipses provide a rapidly changing solar radiation environment. These changes can be studied using simple photodiode sensors, if the radiation reaching the sensors is unaffected by cloud.Transporting the sensors aloft using standard meteorological instrument packages modified to carry extra sensors, provides one promising but hitherto unexploited possibility for making solar eclipse radiation measurements. For the 20th March 2015 solar eclipse, a coordinated campaign of balloon-carried solar radiation measurements was undertaken from Reading (51.44N, 0.94W), Lerwick (60.15N, 1.13W) and Reykjavik (64.13N, 21.90W), straddling the path of the eclipse.The balloons reached sufficient altitude at the eclipse time for eclipse-induced variations in solar radiation and solar limb darkening to be measured above cloud. Because the sensor platforms were free to swing, techniques have been evaluated to correct the measurements for their changing orientation. In the swing-averaged technique, the mean value across a set of swings was used to approximate the radiation falling on a horizontal surface; in the swing-maximum technique, the direct beam was estimated by assuming the sensing surface becomes normal to the solar beam direction at a maximum swing. Both approaches, essentially independent,give values that agree with theoretical expectations for the eclipse-induced radiation changes.

Exploiting existing ground-based remote sensing networks to improve high-resolution weather forecasts

A new generation of high-resolution (1 km) forecast models promises to revolutionize the prediction of hazardous weather such as windstorms, flash floods, and poor air quality. To realize this promise, a dense observing network, focusing on the lower few kilometers of the atmosphere, is required to verify these new forecast models with the ultimate goal of assimilating the data. At present there are insufficient systematic observations of the vertical profiles of water vapor, temperature, wind, and aerosols; a major constraint is the absence of funding to install new networks. A recent research program financed by the European Union, tasked with addressing this lack of observations, demonstrated that the assimilation of observations from an existing wind profiler network reduces forecast errors, provided that the individual instruments are strategically located and properly maintained. Additionally, it identified three further existing European networks of instruments that are currently underexploited, but with minimal expense they could deliver quality-controlled data to national weather services in near–real time, so the data could be assimilated into forecast models. Specifically, 1) several hundred automatic lidars and ceilometers can provide backscatter profiles associated with aerosol and cloud properties and structures with 30-m vertical resolution every minute; 2) more than 20 Doppler lidars, a fairly new technology, can measure vertical and horizontal winds in the lower atmosphere with a vertical resolution of 30 m every 5 min; and 3) about 30 microwave profilers can estimate profiles of temperature and humidity in the lower few kilometers every 10 min. Examples of potential benefits from these instruments are presented.

Can site and landscape-scale environmental attributes buffer bird populations against weather events?

Projected impacts of climate change on the populations and distributions of species pose a challenge for conservationists. In response, a number of adaptation strategies to enable species to persist in a changing climate have been proposed. Management to maximise the quality of habitat at existing sites may reduce the magnitude or frequency of climate-driven population declines. In addition large-scale management of landscapes could potentially improve the resilience of populations by facilitating inter-population movements. A reduction in the obstacles to species’ range expansion, may also allow species to track changing conditions better through shifts to new locations, either regionally or locally. However, despite a strong theoretical base, there is limited empirical evidence to support these management interventions. This makes it difficult for conservationists to decide on the most appropriate strategy for different circumstances. Here extensive data from long-term monitoring of woodland birds at individual sites are used to examine the two-way interactions between habitat and both weather and population count in the previous year. This tests the extent to which site-scale and landscape-scale habitat attributes may buffer populations against variation in winter weather (a key driver of woodland bird population size) and facilitate subsequent population growth. Our results provide some support for the prediction that landscape-scale attributes (patch isolation and area of woodland habitat) may influence the ability of some woodland bird species to withstand weather-mediated population declines. These effects were most apparent among generalist woodland species. There was also evidence that several, primarily specialist, woodland species are more likely to increase following population decline where there is more woodland at both site and landscape scales. These results provide empirical support for the concept that landscape-scale conservation efforts may make the populations of some woodland bird species more resilient to climate change. However in isolation, management is unlikely to provide a universal benefit to all species.

Understanding climate change projections for precipitation over western Europe with a weather typing approach

Precipitation over western Europe (WE) is projected to increase (decrease) roughly northward (equatorward) of 50°N during the 21st century. These changes are generally attributed to alterations in the regional large-scale circulation, e.g., jet stream, cyclone activity, and blocking frequencies. A novel weather typing within the sector (30°W–10°E, 25–70°N) is used for a more comprehensive dynamical interpretation of precipitation changes. A k-means clustering on daily mean sea level pressure was undertaken for ERA-Interim reanalysis (1979–2014). Eight weather types are identified: S1, S2, S3 (summertime types), W1, W2, W3 (wintertime types), B1, and B2 (blocking-like types). Their distinctive dynamical characteristics allow identifying the main large-scale precipitation-driving mechanisms. Simulations with 22 Coupled Model Intercomparison Project 5 models for recent climate conditions show biases in reproducing the observed seasonality of weather types. In particular, an overestimation of weather type frequencies associated with zonal airflow is identified. Considering projections following the (Representative Concentration Pathways) RCP8.5 scenario over 2071–2100, the frequencies of the three driest types (S1, B2, and W3) are projected to increase (mainly S1, +4%) in detriment of the rainiest types, particularly W1 (−3%). These changes explain most of the precipitation projections over WE. However, a weather type-independent background signal is identified (increase/decrease in precipitation over northern/southern WE), suggesting modifications in precipitation-generating processes and/or model inability to accurately simulate these processes. Despite these caveats in the precipitation scenarios for WE, which must be duly taken into account, our approach permits a better understanding of the projected trends for precipitation over WE.

Understanding advances in the simulation of the Madden-Julian Oscillation in a numerical weather prediction model.

The Madden-Julian Oscillation (MJO) is the dominant mode of intraseasonal variability in the Trop- ics. It can be characterised as a planetary-scale coupling between the atmospheric circulation and organised deep convection that propagates east through the equatorial Indo-Pacific region. The MJO interacts with weather and climate systems on a near-global scale and is a crucial source of predictability for weather forecasts on medium to seasonal timescales. Despite its global signifi- cance, accurately representing the MJO in numerical weather prediction (NWP) and climate models remains a challenge. This thesis focuses on the representation of the MJO in the Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasting (ECMWF), a state-of-the-art NWP model. Recent modifications to the model physics in Cycle 32r3 (Cy32r3) of the IFS led to ad- vances in the simulation of the MJO; for the first time the observed amplitude of the MJO was maintained throughout the integration period. A set of hindcast experiments, which differ only in their formulation of convection, have been performed between May 2008 and April 2009 to asses the sensitivity of MJO simulation in the IFS to the Cy32r3 convective parameterization. Unique to this thesis is the attribution of the advances in MJO simulation in Cy32r3 to the mod- ified convective parameterization, specifically, the relative-humidity-dependent formulation for or- ganised deep entrainment. Increasing the sensitivity of the deep convection scheme to environmen- tal moisture is shown to modify the relationship between precipitation and moisture in the model. Through dry-air entrainment, convective plumes ascending in low-humidity environments terminate lower in the atmosphere. As a result, there is an increase in the occurrence of cumulus congestus, which acts to moisten the mid-troposphere. Due to the modified precipitation-moisture relationship more moisture is able to build up which effectively preconditions the tropical atmosphere for the transition to deep convection. Results from this thesis suggest that a tropospheric moisture control on convection is key to simulating the interaction between the physics and large-scale circulation associated with the MJO.

Exploiting satellite-based rainfall for weather index insurance: the challenges of spatial and temporal aggregation

Lack of access to insurance exacerbates the impact of climate variability on smallholder famers in Africa. Unlike traditional insurance, which compensates proven agricultural losses, weather index insurance (WII) pays out in the event that a weather index is breached. In principle, WII could be provided to farmers throughout Africa. There are two data-related hurdles to this. First, most farmers do not live close enough to a rain gauge with sufficiently long record of observations. Second, mismatches between weather indices and yield may expose farmers to uncompensated losses, and insurers to unfair payouts – a phenomenon known as basis risk. In essence, basis risk results from complexities in the progression from meteorological drought (rainfall deficit) to agricultural drought (low soil moisture). In this study, we use a land-surface model to describe the transition from meteorological to agricultural drought. We demonstrate that spatial and temporal aggregation of rainfall results in a clearer link with soil moisture, and hence a reduction in basis risk. We then use an advanced statistical method to show how optimal aggregation of satellite-based rainfall estimates can reduce basis risk, enabling remotely sensed data to be utilized robustly for WII.

The use of remotely sensed rainfall for managing drought risk: a case study of weather index insurance in Zambia

Remotely sensed rainfall is increasingly being used to manage climate-related risk in gauge sparse regions. Applications based on such data must make maximal use of the skill of the methodology in order to avoid doing harm by providing misleading information. This is especially challenging in regions, such as Africa, which lack gauge data for validation. In this study, we show how calibrated ensembles of equally likely rainfall can be used to infer uncertainty in remotely sensed rainfall estimates, and subsequently in assessment of drought. We illustrate the methodology through a case study of weather index insurance (WII) in Zambia. Unlike traditional insurance, which compensates proven agricultural losses, WII pays out in the event that a weather index is breached. As remotely sensed rainfall is used to extend WII schemes to large numbers of farmers, it is crucial to ensure that the indices being insured are skillful representations of local environmental conditions. In our study we drive a land surface model with rainfall ensembles, in order to demonstrate how aggregation of rainfall estimates in space and time results in a clearer link with soil moisture, and hence a truer representation of agricultural drought. Although our study focuses on agricultural insurance, the methodological principles for application design are widely applicable in Africa and elsewhere.

Large reorganizations in butterfly communities during an extreme weather event

Drought events are projected to increase in frequency and magnitude, which may alter the composition of ecological communities. Using a functional community metric that describes abundance, life history traits and conservation status, based upon Grime’s CSR (Competitive-Stress tolerant-Ruderal)¬ scheme, we investigated how British butterfly communities changed during an extreme drought in 1995. Throughout Britain, the total abundance of these insects had a significant tendency to increase, accompanied by substantial changes in community composition, particularly in more northerly, wetter sites. Communities tended to shift away from specialist, vulnerable species, and towards generalist, widespread species and, in the year following, communities had yet to return to equilibrium. Importantly, heterogeneity in surrounding landscapes mediated community responses to the drought event. Contrary to expectation, however, community shifts were more extreme in areas of greater topographic diversity, whilst land-cover diversity buffered community changes and limited declines in vulnerable specialist butterflies.

Extended time weather forecasts contributes to agricultural productivity estimates

Weather conditions in critical periods of the vegetative crop development influence crop productivity, thus being a basic parameter for crop forecast. Reliable extended period weather forecasts may contribute to improve the estimation of agricultural productivity. The production of soybean plays an important role in the Brazilian economy, because this country is ranked among the largest producers of soybeans in the world. This culture can be significantly affected by water conditions, depending on the intensity of water deficit. This work explores the role of extended period weather forecasts for estimating soybean productivity in the southern part of Brazil, Passo Fundo, and Londrina (State of Rio Grande do Sul and Parana, respectively) in the 2005/2006 harvest. The goal was to investigate the possible contribution of precipitation forecasts as a substitute for the use of climatological data on crop forecasts. The results suggest that the use of meteorological forecasts generate more reliable productivity estimates during the growth period than those generated only through climatological information.