Diagnosis and impact of time variations of regionally averaged background error covariances

Tese de doutoramento, Ciências Geofisicas e da Geoinformação (Meteorologia), Universidade de Lisboa, Faculdade de Ciências, 2012Current data assimilation systems aim at produce the best possible estimate of the atmospheric state to be used as initial conditions by a forecasting model. This estimate is called the model analysis. In the formalism of the Three-Dimensional Variational Data Assimilation (3D-Var), the analysis should minimize a quadratic cost function that measures the distance between the estimate and the available information, namely the observations and the background, taking into account their respective precisions. Observation error covariances contain information about errors in the observation process (measurement and representativeness uncertainties). Background error covariances are used to filter and propagate the observational information in a spatial multivariate way. They compose the gain matrix that determines how the analysis increments (that is to say, the analysis corrections to the background) are obtained from the innovations (i.e., the differences between observations and background at the observation locations). However, since the true atmospheric state can not be exactly known, background error covariances (in particular) can only be estimated. Nowadays, Numerical Weather Prediction (NWP) centers often use an off-line specification of background error covariances. This relies on running an ensemble of perturbed assimilation cycles during a past period, to simulate the error evolution during the successive analysis/forecast steps. Moreover, as the full background error covariance matrix is far too large to be handled explicitly, sparse covariance models are usually employed, and they are calibrated by using ensemble forecast perturbations. These sparse covariance models are often based on simplifications such as horizontal homo geneity and temporal stationarity. This is the case of the ALADIN/France regional system which has been used in this study. The impact of seasonal and daily variations are studied. Results indicate that specifying background error covariances corresponding to a one-day sliding average (preceding each each analysis date) has a positive impact on the short-range forecast quality, compared to the currently operational static covariances. This positive impact arises to a large extent from the update of the monthly component of covariance variations. The update of the daily component contributes to additional positive impacts, which are however relatively localized and modest during this period. These impacts are illustrated by case studies for humidity during an anticyclonic situation, and for wind during a cyclonic event. These results support the idea to consider an on-line updated specification of background error covariances.Em previsão numérica do tempo (PNT), um sistema de assimilação de dados tem como objetivo produzir a melhor estimativa possível do estado da atmosfera num dado instante utilizando toda a informação relevante disponível. Esta estimativa ´e conhecida como ”análise” e visa fornecer condições iniciais de qualidade a um modelo de previsão numérica. Como informação relevante consideram-se tipicamente as observações e uma estimativa conhecida a priori que normalmente corresponde a uma previsão de curto alcance, obtida por integração do modelo numérico a partir de uma análise anterior. As observações são de dois tipos: as observações in situ (como são as observações de altitude resultantes de radiossondagens e as observações de superfície obtidas a partir de uma rede de estacões assentes sobre a superfície terrestre) e por deteção remota (como são as radiações medidas a partir de satélites geostacionários ou de ´orbita polar e ainda as refletividades medidas por radares meteorológicos). No formalismo da assimilação variacional tri-dimensional conhecido como 3D-Var, a análise resulta da minimização de uma função custo quadrática que mede a distância da análise às observações e à estimativa a priori tomando em consideração a precisão com que estas fontes de informação são conhecidas. Em particular, é utilizada a covariância dos erros das observações. Esta covariância contêm a informação sobre os erros de medição e de representatividade que afetam as observações. É também utilizada a covariância dos erros da estimativa a priori com a função de filtrar e propagar, espacialmente e de forma multivariada, a informação observada. Estas duas entidades, a matriz de covariância dos erros das observações e a matriz de covariância dos erros da estimativa a priori, compõem a chamada ”matriz ganho” da equação da análise. Esta equação determina como é que as correções à estimativa a priori (i.e., os incrementos da análise) são obtidas a partir das inovações (i.e., as diferenças entre as observações e a estimativa a priori nos locais das observações). Contudo, dado que o estado exato da atmosfera não pode ser conhecido, também as covariâncias dos erros apenas podem ser estimadas com base em hipóteses que só podem ser confirmadas, ou não, a posteriori em amostras independentes daquelas onde se calibram as estatísticas dos erros. Este é um dos principais desafios científicos da assimilação de dados na atualidade. Os centros modernos de PNT usam frequentemente uma especificação da covariância dos erros da estimativa a priori que é obtida por processos independentes do ciclo de assimilação em tempo não-real. Dado que não varia ao longo do ciclo de assimilação, diz-se tratar-se de uma especificação de tipo ”estático”. Além disso, recorrem a técnicas de ensemble baseadas na perturbação do ciclo de assimilação durante um determinado período de tempo (passado) para simular a evolução dos erros ao longo dos diversos passos da análise e da previsão (por dizer respeito a estados passados da atmosfera, esta especificação é vulgarmente designada de ”climatológica”). Como a matriz da covari ância dos erros da estimativa a priori é demasiado grande para ser manipulada de forma explícita, os centros de PNT também empregam modelos que envolvem apenas matrizes esparsas de covariâncias, os quais são calibrados a partir de ensembles de previsões perturbadas usando metodologias mais ou menos simplificadas e eventualmente sub-optimizadas. Muito frequentemente, estes modelos são baseados em simplificações, como são as da homogeneidade espacial e a da estacionaridade dos erros, que inibem a representação da dependência da covariância com a evolução da situação meteorológica. Em particular, esta inibição ´e intrínseca `a atual versão operacional do modelo de área limitada ALADIN/France utilizado neste estudo. Esta tese em Assimilação de Dados tem como objetivo principal demonstrar, num contexto real de PNT, a importância duma representação adequada das variações temporais da covariância do erro da estimativa a priori que é utilizada num sistema de área limitada. Tendo como base o sistema numérico de área limitada ALADIN/France, este estudo evidencia claramente o efeito positivo resultante da utilização de uma especificação dessas estimativas em tempo- (quasi.) real. A simulação dos erros da estimativa a priori foi efetuada por técnicas de ensemble sob a hipótese de que o modelo de previsão é perfeito, isto é , de que não existe qualquer erro do modelo (determinista ou estocástico) e para qualquer membro do ensemble. Os erros assim estimados foram utilizados para calibrar o modelo de covariâncias esparsas utilizadas no sistema ALADIN/France. A primeira fase do trabalho, descrita porMonteiro & Berre (2010), visou a generalização da hipótese de estacionaridade utilizada no cálculo das covariâncias dos erros da estimativa a priori (previsões a 6 horas), através do diagnóstico da sua variação temporal. Com base nessas estimativas, foram igualmente calculadas escalas integrais de correlação horizontal e vertical. Foi efetuado o diagnóstico da variação temporal nas estimativas da covariância em função da mudança da estacão do ano (inverno versus verão), do dia (em conexão com a mudança da situação sinóptica) e da hora (relacionada com o ciclo diurno). Para tal consideraram-se dois períodos de um mês, um no inverno e outro no verão, e em cada um destes períodos construiram-se dois sistemas de ensembles de 6 membros, os quais resultaram da perturbação independente do mesmo conjunto de observações. Esta duplicação permitiu confirmar a robustez das estatísticas. De uma forma geral, verificou-se que no verão as variâncias dos erros tendem a ser superiores às que se observam no inverno (para os parâmetros da temperatura, humidade relativa e vento). Em particular, no verão registaram-se correlações que são mais estreitas horizontalmente e mais extensas verticalmente e que estão relacionadas com o aumento da atividade convetiva na região geográfica em estudo (em comparação com a que se observa no inverno). No que respeita `as varia¸c˜oes di´arias verificou-se (no per´ıodo de inverno em estudo) que o desvio padrão do erro a priori ´e em geral maior quando a situação sinóptica tem maior instabilidade baroclínica (por exemplo, em situações de desenvolvimento depressionário) particularmente no inverno, sendo acompanhada de redução do comprimento de correlação horizontal do erro no caso da humidade e da temperatura. Além disso, observou-se que as variações diárias da variância do error são por vezes mais acentuadas do que as variações sazonais (se compararmos covariâncias para uma situação anticiclónica de inverno com as de um caso depressionário de inverno, por exemplo). Finalmente, verificou-se que as variações das covariâncias ao longo de um ciclo diurno são significativas na camada limite da atmosfera no período de verão: os desvios padrão tendem a ser maiores para as previsões válidas ao 18 UTC, quando a escala do comprimento da correlação horizontal é reduzida (especialmente para os parâmetros da humidade e da temperatura) e as funções de correlação vertical são extensas, sendo este um efeito esperado, dado o aumento da atividade convetiva que acontece com o aquecimento da superfície terrestre durante a tarde, sobre o domínio geográfico em causa. Na segunda parte do trabalho, foi estudado o efeito da variação sazonal e diária das matrizes de covariância do erro a priori sobre a qualidade das previsões do sistema ALADIN/France ao longo de um mês de inverno. Para tal realizaram-se três experiencias separadas. Na primeira consideraram-se as covariâncias calculadas a partir de uma média mensal (extática) ao longo de um período passado (esta experiencia reproduz as condições do sistema operacional em que a covariância climatológica é referente a um período de outono); na segunda, as covariâncias foram calculadas a partir de uma média mensal (extática) sobre o período de tempo em estudo (inverno); na terceira, as covariâncias foram calculadas a partir de uma média diária móvel (precedente a cada data da análise). Os resultados indicaram que a especificação das covariâncias dos erros da estimativa a priori correspondente a uma média diária móvel tem um efeito positivo na qualidade da previsão de curto prazo (para alcances entre as 12 e 18 h, para a temperatura e vento e até às 24 h para a humidade) quando comparada com a qualidade resultante de uma especificação estática climatológica (a utilizada no atual sistema operacional). Este efeito positivo resulta principalmente da atualização sazonal (do mês de outono para o mês de inverno) das covariâncias. A atualização diária contribui também para um efeito positivo adicional mas este é mais localizado e modesto. O efeito da variação diária é ilustrado através de dois casos de estudo, verificados durante o mês de inverno: uma situação anticiclónica em que a melhoria é nítida sobre a humidade e um evento ciclónico em que a melhoria é mais evidente sobre o campo do vento. Neste caso, regista-se uma melhoria da previsão extremos espaciais do vento a prazos até às 36 h. Em conclusão, os resultados obtidos sustentam a ideia de que é adequado implementar uma especificação em tempo- (quasi) real das covariâncias do erro da estimativa a priori, em substituição da atual aproximação estática climatológica e, tal como foi visto na primeira parte do trabalho, um ensemble de 6 membros já permite obter estimativas diárias robustas a um baixo custo computacional, apesar das muitas melhorias metodológicas que ainda podem ser feitas

On the viability of dc homes: an economic perspective from domestic electrical appliances

The past few years witnessed a growing acclaim for dc power systems, which is mainly justified by the increasing use of energy storage systems and renewable energy sources based mainly on solar photovoltaic technologies. However, there is also a motivation from the point of view of domestic electrical appliances. Since the vast majority of these appliances is comprised by an ac-dc converter, it can be convenient to shift the domestic power supply from ac to dc. In this context, this paper presents an economic assessment of dc homes from the energy consumption perspective and its comparison with traditional homes supplied by ac electrical power grids. In order to perform such assessment, the main type of electronic loads is powered both by ac voltage and by dc voltage, comparing the efficiency and estimated energy cost for each case. The removal of the ac-dc converter present in these loads is also analyzed and compared with the two previously referred cases, supporting the supply of dc power to this type of loads. The analysis is performed by means of experimental results obtained with a laboratorial setup, aiming to validate the feasibility of dc homes under realistic operating conditions of the loads.This work has been supported by FCT - Fundacao para a Ciencia e Tecnologia within the Project Scope: UID/CEC/00319/2019. This work has been supported by FCT within the Project Scope DAIPESEV -Development of Advanced Integrated Power Electronic Systems for Electric Vehicles: PTDC/EEI-EEE/30382/2017. This work is part of the FCT project 0302836 NORTE-01-0145-FEDER-030283. Mr. Tiago Sousa is supported by the doctoral scholarship SFRH/BD/134353/2017 granted by the Portuguese FCT agency

Robot-assisted rehabilitation architecture supported by a distributed data acquisition system

Rehabilitation robotics aims to facilitate the rehabilitation procedure for patients and physical therapists. This field has a relatively long history dating back to the 1990s; however, their implementation and the standardisation of their application in the medical field does not follow the same pace, mainly due to their complexity of reproduction and the need for their approval by the authorities. This paper aims to describe architecture that can be applied to industrial robots and promote their application in healthcare ecosystems. The control of the robotic arm is performed using the software called SmartHealth, offering a 2 Degree of Autonomy (DOA). Data are gathered through electromyography (EMG) and force sensors at a frequency of 45 Hz. It also proves the capabilities of such small robots in performing such medical procedures. Four exercises focused on shoulder rehabilitation (passive, restricted active-assisted, free active-assisted and Activities of Daily Living (ADL)) were carried out and confirmed the viability of the proposed architecture and the potential of small robots (i.e., the UR3) in rehabilitation procedure accomplishment. This robot can perform the majority of the default exercises in addition to ADLs but, nevertheless, their limits were also uncovered, mainly due to their limited Range of Motion (ROM) and cost.info:eu-repo/semantics/publishedVersio

Angle assessment for upper limb rehabilitation: a novel light detection and ranging (LiDAR)-based approach

The accurate measurement of joint angles during patient rehabilitation is crucial for informed decision making by physiotherapists. Presently, visual inspection stands as one of the prevalent methods for angle assessment. Although it could appear the most straightforward way to assess the angles, it presents a problem related to the high susceptibility to error in the angle estimation. In light of this, this study investigates the possibility of using a new approach to angle calculation: a hybrid approach leveraging both a camera and LiDAR technology, merging image data with point cloud information. This method employs AI-driven techniques to identify the individual and their joints, utilizing the cloud-point data for angle computation. The tests, considering different exercises with different perspectives and distances, showed a slight improvement compared to using YOLO v7 for angle calculation. However, the improvement comes with higher system costs when compared with other image-based approaches due to the necessity of equipment such as LiDAR and a loss of fluidity during the exercise performance. Therefore, the cost-benefit of the proposed approach could be questionable. Nonetheless, the results hint at a promising field for further exploration and the potential viability of using the proposed methodology.This work has been supported by SmartHealth—Inteligência Artificial para Cuidados de Saúde Personalizados ao Longo da Vida, under the project number NORTE-01-0145-FEDER- 000045. The authors are grateful to the Foundation for Science and Technology (FCT, Portugal) for financial support through national funds FCT/MCTES (PIDDAC) to CeDRI (UIDB/05757/2020 and UIDP/05757/2020) and SusTEC (LA/P/0007/2021). Arezki A. Chellal is grateful to the FCT Foundation for its support through the FCT PhD scholarship with reference UI/BD/154484/2022. João Braun is grateful to the FCT Foundation for its support through the FCT PhD scholarship with reference 2023.04536.BD.info:eu-repo/semantics/publishedVersio

Influence of hormonal replacement therapy in lipid peroxidation levels of postmenopausal women with different cardiovascular capacity

It has been suggested that exercise has a positive impact on the prevention and progression of cardiovascular disease (CVD). One of the main mechanisms is through the modification of lipoprotein levels and the risk of its oxidation, especially LDL lipoproteins. After menopause, women experience an increased incidence of cardiovascular disease. In contrast, women receiving hormonal replacement therapy (HRT) seem to be protected. The aim of this study was to infer how HRT affect lipid peroxidation levels in postmenopausal women with different levels of aerobic fitness. Design & Method: Sixty four women participate in this study, 32 of them receive HRT (group with HRT – GWHRT) (average age¼55.9 years, average weight¼ 66.9 kg and average high¼156.0 cm) and the remained 32 women didn’t receive HRT (group without HRT – GWOHRT) (average age¼61.0 years, average weight¼ 67.6 kg and average high¼154.3 cm). Total cholesterol (mg dL71), HDL-cholesterol (mg dL71), LDL-cholesterol (mg dL71) and triglycerides levels (mg dL71) have been analyzed in serum obtained from a blood sample collected after 8 hours of fasting, and measured in Dr. Lange LP20 according to the specific manufacturer instructions. Serum MDA concentration (ng L71) was determined by spectrophotometric method. Aerobic capacity (VO2max ml kg71 min71) was assessed according to an adaptation of Bruce protocol. Differences between groups were tested through Student t-test. A Spearman correlation was performed in order to test variables associations. Significance level was established at 5%.Results: Our results have found differences between groups in age (t¼3.018; p50.01), in VO2max (t¼73.774; p50.01) and in serum MDA concentration (t¼6.750; p50.01). The GWHRT were younger, had a higher VO2max (31.38 for GWHRT and 26.19 for GWOHRT), and had lower levels of serum MDA concentration (0.29 for GWHRT and 0.73 for GWOHRT) comparatively with those women from the GWOHRT. However, our results failed to find any differences between groups regarding serum triglycerides, total cholesterol, HDL-cholesterol, LDL-cholesterol or BMI. In this study, serum MDA concentration didn’t correlate with higher levels of lipid profile, as we might have expected, but correlate inversely with HRT (r¼7.726, p¼.00) and with VO2max (r¼7.287, p¼.02). Conclusion: Our results suggest that HRT should exert an antioxidant protective effect against lipid peroxidation, as well as exercise perhaps through the stimulation of antioxidant capacity

A proactive approach to the conservation of historic and cultural Heritage: The HeritageCare methodology

Presently, no systematic policy for the preventive conservation of the built cultural heritage exists in South-West Europe. Current approaches for inspection, diagnosis, monitoring and reactive conservation are normally intermittent, unplanned, expensive and lack methodical strategy. The available financial resources are scarce and are mostly addressed to listed buildings. Besides, owners and stakeholders often reveal reluctance to invest in preventive conservation and maintenance programs. In view of these considerations, and driven by the principle “prevention is better than cure”, the HeritageCare project has developed a system for the preventive conservation and maintenance of the built heritage. The main aim of this paper is to briefly describe the methodology, including its three levels of service, and present the main results of the implementation and validation of the service level 1 on a case study belonging to the Portuguese architectural heritage.This work was carried out within the scope of the project HeritageCare (SOE1/P5/P0258), co-funded by the Interreg-Sudoe/FEDER program and included in the research activities of the ISISE Research Centre, also financed by FEDER funds through the Competitiveness Factors Operational Program – COMPETE and by national funds through FCT – Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER-007633. Authors would like to express their gratitude to the Centre for Computer Graphics, HeritageCare partner, for the development of the platform (and supporting database) and the mobile application, outputs of the project HeritageCare. Authors would like to express their gratitude to the Santa Maria de la Real Foundation, HeritageCare partner, for the placement of the monitoring system at the Ducal Palace, Guimarães, Portugal

A methodological approach to potential vegetation modeling using GIS techniques and phytosociological expert-knowledge: application to mainland Portugal

An attempt to obtain a consistent spatial model of natural potential vegetation (NPV) for the mainland Portuguese territory is reported. Spatial modeling procedures performed in a Geographic Information System (GIS) environment, aimed to operationalize phytosociological expert-knowledge about the putative distribution of potential zona1 forest communities dominam in the Portuguese continental territories. The paradigm for NPV assumed was that of RIVAS-MARTINE(1Z9 76) and RIVAS-MARTINEeZt al. (1999), which presupposes, for a given territory, a univocal correspondence between a uniform combination of bioclimatic stage and lithology' gi ven a biogeographical context, and a unique successional sequence leading to a single climax community (i. e. a vegetation series (VS)). Information issued from both literature and a team of phytosociologists possessing detailed knowledge about Portuguese vegetation, namely about forests and its seria1 vegetation, was acknowledged as a starting point for the construction of such a habitat-vegetation correspondence model. First, a bioclimatic map concerning the "Worldwide Bioclimatic Classification System" (WBCS) of RIVAS-MARTINE(1Z9 81 -2004), obtained by multivariate grostatistical interpolation issuing from the work of MESQUITA(2 005), was set. Severa1 partia1 matrices, one for each biogeographical Province, combined such habitat statements to VS. Initial incoherence due to vagueness of statements led to an important amount of both superimposition of VS and habitat gaps in the matrices. Further rearrangement of the table according to known field distribution of VS by experts allowed setting an approximate univocal correspondence VS-habitat. Finally, an intersection of bioclimatic, lithology and biogeographic maps yielded over a thousand habitat combinations to be associated each to a single VS through implementation of the matrices as a set of rules. Again, inconsistencies were solved likewise, but this time by direct observation of the map by experts. Keeping of phytosociological consistency and fidelity to information on actual vegetation field distribution was always mandatory during the proces

Effect of the sodium reduction and smoking system on quality and safety of smoked salmon (Salmo salar)

Excessive sodium (Na) intake has been associated with high blood pressure and cardiovascular diseases. Therefore, sodium reduction is a public health challenge worldwide. The aim of this study was to develop smoked salmon with a reduced Na content. Sodium chloride (NaCl) was replaced by potassium chloride (KCl) at 25% and 50% (molar replacement) and studied in combination with two smoking procedures (natural wood and liquid smoke) as well as two smoking temperatures (18-19ºC or 56ºC). Smoked salmon samples were characterized by physicochemical, sensory and microbiological analyses. No major differences were observed regarding physicochemical properties in the studied treatments. Smoked samples with 50% of NaCl replaced by KCl were slightly more bitter than those with 25% whereas samples with 25% of replacement did not show differences to those with non-reduced Na content (5 g of added NaCl per 100 g of salmon). Molar Na:K ratio decreased from 4,3 in controls to 1,4 and 0,6 in samples with a NaCl reduction level of 25% and 50 % respectively. Microbiological assessment indicates that 2-week shelf-life would be appropriate and safe in terms of accomplishment of the EU regulation, taking into account foreseeable storage temperatures (up to 8 ºC). Thus, it is possible to achieve a reduction of 25-50% of NaCl in smoked salmon by replacing NaCl by KCl and considerer this product as a “source” of K.info:eu-repo/semantics/acceptedVersio

Effect of the sodium reduction and smoking system on quality and safety of smoked salmon (Salmo salar)

Excessive sodium (Na) intake has been associated with high blood pressure and cardiovascular diseases. Therefore, sodium reduction is a public health challenge worldwide. The aim of this study was to develop smoked salmon with a reduced Na content. Sodium chloride (NaCl) was replaced by potassium chloride (KCl) at 25% and 50% (molar replacement) and studied in combination with two smoking procedures (natural wood and liquid smoke) as well as two smoking temperatures (18-19ºC or 56ºC). Smoked salmon samples were characterized by physicochemical, sensory and microbiological analyses. No major differences were observed regarding physicochemical properties in the studied treatments. Smoked samples with 50% of NaCl replaced by KCl were slightly more bitter than those with 25% whereas samples with 25% of replacement did not show differences to those with non-reduced Na content (5 g of added NaCl per 100 g of salmon). Molar Na:K ratio decreased from 4,3 in controls to 1,4 and 0,6 in samples with a NaCl reduction level of 25% and 50 % respectively. Microbiological assessment indicates that 2-week shelf-life would be appropriate and safe in terms of accomplishment of the EU regulation, taking into account foreseeable storage temperatures (up to 8 ºC). Thus, it is possible to achieve a reduction of 25-50% of NaCl in smoked salmon by replacing NaCl by KCl and considerer this product as a “source” of K.info:eu-repo/semantics/acceptedVersio

A fabric-based soft hand exoskeleton for assistance: the ExHand Exoskeleton

INTRODUCTION: The rise of soft robotics has driven the development of devices for assistance in activities of daily living (ADL). Likewise, different types of actuation have been developed for safer human interaction. Recently, textile-based pneumatic actuation has been introduced in hand exoskeletons for features such as biocompatibility, flexibility, and durability. These devices have demonstrated their potential use in assisting ADLs, such as the degrees of freedom assisted, the force exerted, or the inclusion of sensors. However, performing ADLs requires the use of different objects, so exoskeletons must provide the ability to grasp and maintain stable contact with a variety of objects to lead to the successful development of ADLs. Although textile-based exoskeletons have demonstrated significant advancements, the ability of these devices to maintain stable contact with a variety of objects commonly used in ADLs has yet to be fully evaluated. MATERIALS AND METHODS: This paper presents the development and experimental validation in healthy users of a fabric-based soft hand exoskeleton through a grasping performance test using The Anthropomorphic Hand Assessment Protocol (AHAP), which assesses eight types of grasping with 24 objects of different shapes, sizes, textures, weights, and rigidities, and two standardized tests used in the rehabilitation processes of post- stroke patients. RESULTS AND DISCUSSION: A total of 10 healthy users (45.50 ± 14.93 years old) participated in this study. The results indicate that the device can assist in developing ADLs by evaluating the eight types of grasps of the AHAP. A score of 95.76 ± 2.90% out of 100% was obtained for the Maintaining Score, indicating that the ExHand Exoskeleton can maintain stable contact with various daily living objects. In addition, the results of the user satisfaction questionnaire indicated a positive mean score of 4.27 ± 0.34 on a Likert scale ranging from 1 to 5