Ashley Edward Roy Soosay

Narayanan Kulathuramaiyer

TRIZ-based Remodeling of Multiple True-False Questions

Keywords: Multiple True-False Question, TRIZ, Knowledge-based modelling

In light of the COVID-19, medical education is widely transitioning to a fully online mode. This change poses challenges on ensuring valid assessments for medical education. Within the constraints of online assessment scenario, the academic rigour has to be maintained, while at the same time, enabling a remote administration of student learning activities. A TRIZbased approach has been adopted in addressing this contradiction. We used TRIZ tools such as Functional Analysis, Cause and Effect Chain Analysis, Engineering and Physical contradiction to model the problem. The TRIZ knowledge models, particularly through the recommended Inventive Principles has provided insightful directions as research ideas. This paper then explored a combined validation method based on the assessment activities conducted in the medical faculty during the COVID-19 lockdown. The hybridized TRIZ mode has served as an excellent knowledge elicitation framework for addressing this long-standing problem.

Introduction

The COVID-19 pandemic has been the impetus for medical education in preclinical years going totally online. The declaration of COVID-19 as a worldwide pandemic [START_REF] Bahaeldin | Al-Qahatani and Ismaeel Satti, Online assessment for the final year medical students during COVID-19 pandemics; the exam quality and students' performance[END_REF] has led to the Movement Control Order (MCO) in Malaysia [START_REF] Bunyan | PM: Malaysia under movement control order from Wed until March 31, all shops closed except for essential services[END_REF][START_REF] Jun | Movement control order not a lockdown, says former health minister[END_REF][START_REF] Sukumaran | Malaysia in partial lockdown to limit coronavirus spread[END_REF][START_REF] Tang | Movement as an effective measure against Covid-19 spread in Malaysia: an overview[END_REF], which in turn has forced institutions of learning to adopt and adapt new norm in teaching and learning (T&L) process. The COVID-19 outbreak not only challenged the learners but also the T&L service providers to switch from face to face (F2F) classroom settings to remote learning (RL) [START_REF] Ahmed | COVID-19 and medical education. The Lancet[END_REF][START_REF] Alsafi | The coronavirus (COVID-19) pandemic: Adaptations in medical education[END_REF]. The mental well-being of people worldwide is affected by this pandemic [START_REF] Wang | The impact of COVID-19 pandemic on physical and mental health of Asians: A study of seven middle-income countries in Asia[END_REF]. The outbreak has thus resulted an unparalleled instructional environment. Many institutions have provided internet access to their students and lecturers in an attempt to facilitate a smooth transition to the new pedagogy which largely relies on the quality of internet connectivity [START_REF] Serhan | Transitioning from Face-to-Face to Remote Learning: Students' Attitudes and Perceptions of Using Zoom during COVID-19 Pandemic[END_REF]. Mastering the use of online communication platform has been a pivotal factor to ensure success in the design of an engaging RL. In Universiti Malaysia Sarawak (UNIMAS), T&L is delivered electronically via its online learning management system, e-Learning Enrichment and Advanced Platform (e-LEAP), which is based on Moodle platform. Synchronous and asynchronous T&L is being conducted with recorded lectures, remote problem based learning (PBL) sessions and clinical video sessions serving as the pedagogy of RL.

What comes hand in hand with T&L is assessment. With such constraints in administering F2F T&L delivery, online assessment becomes the primary mode of examining students' T&L. Online assessment has therefore taken a paramount role in driving learning, during this challenging period [START_REF] Sabzwari | Rethinking Assessment in Medical Education in the time of COVID-19[END_REF]. The shift from paper-based learning to an online mode has been a drastic change for the Faculty of Medicine & Health Sciences, UNIMAS. The paper-based-assessment which comprised of Multiple Choice Question (True/False) (MTFQ), Best Answer Question (BAQ), Objective Structured Practical Examination (OSPE) and Modified Essay Question (MEQ), was required to be replicated using the eLEAP platform, with reassessment considerations.

The use of MTFQ has been seen suitable for assessing the first three cognitive levels of remembering, comprehending, applying and to a great extent the level of analysis [START_REF] David | E-assessment by design: using multiple-choice tests to good effect[END_REF][START_REF] Costello | The future of online testing and assessment: question quality in MOOCs[END_REF]. At the same time addressing the high failure rates associated with the MTFQ mode of assessment is pertinent. As the ideal choice of assessment methods are still a subject of debate in the academic scenario, this paper presents an insightful dissection of this problem via Theory of Inventive Problem Solving (TRIZ). This paper explores a TRIZ-based approach to model this long-standing problem, in shedding insights on current methods being used as well as to reveal directions for potential innovative solutions. Moreover, the COVID-19 pandemic has presented an opportunity to further examine this modality in our assessment tool using the e-LEAP platform. In this paper we investigate using a case study to achieve an ideal (or innovative) form of assessment suited for medical students.

TRIZ, which has been founded by Genrich Altshuler in the former Soviet Union, has been widely used as a means of solving complex problems [START_REF] Altshuller | The innovation algorithm: TRIZ, systematic innovation and technical creativity[END_REF]. TRIZ was explored as a problem-solving methodology due to its strengths in dealing with complex problems [START_REF] Al-Betar | A TRIZ-inspired bat algorithm for gene selection in cancer classification[END_REF] such as high failure rates in MTFQ assessment among preclinical students. The research project was initially explored as a challenge in a TRIZ training. The main author with over 25 years of experience as a medical educator, was then intrigued by the simplistic Engineering systems model and the analogical reasoning capability that it provided.

The use of tools such as Cause and Effect Chain Analysis (CECA) [START_REF] Swee | Applying Triz for Production Quality Improvement[END_REF], Function Models and Physical Contradictions were explored to shed insights to this longstanding problem. TRIZ has therefore provided the necessary visual modelling tools in assisting to deal with an ill-structured problem.

Research methodology

The modelling of online learning delivery was adopted as a case study, considering the pandemic situation and the forced online evaluation. While at the same time examining a more effective mode for shaping future medical education. Firstly, we reviewed the literature encompassing areas of medical education assessment modalities and then probing the causes for high failure rates in MTFQ. The medical scenario that shaped the research was outlined further and followed by preliminary analysis using Function Analysis and Cause and Effect Chain Analysis. Interviews were then conducted with experts in the field of medical education to validate the logical flow in the cause-effect relationships. The preliminary TRIZ models that guided to contextualize the research was apparent. Table 1 shows the overall concept of this project's methodology. The approach has demonstrated the potential application of these TRIZ tools as a means for knowledge elicitation by interacting with experts to construct knowledge expert models. Subsequently Engineering Contradiction and Physical Contradiction were employed as analytical tools for modelling the problem in an entire new way, shedding insights on the problem at hand. Each of these tools presented a series of inventive principles by applying heuristic approach.

The recommended solutions were mapped and directions for achieving these concepts were contrasted with features within the existing eLEAP platform. The feature analysis provided alternative ways of modelling the modalities. The exploratory approach that employs the series of TRIZ tools is illustrated in Table 1.

Medical Examination in UNIMAS Case Study

During an undergraduate medical training, the clinical practice of prevention, health and wellness is inculcated to future practicing doctors. The difficulty of this training in reality has to deal with a variety of stressors as experienced by the trainees [START_REF] Garber | Sources of stress in a pharmacy student population[END_REF][START_REF] Vyas | Sources of medical student stress[END_REF][START_REF] Hundertmark | Stress and stressors of medical student near-peer tutors during courses: a psychophysiological mixed methods study[END_REF]. Vyas et. al., reported that there is a significant level of stress among the female preclinical year students in Southeastern US allopathic medical school. Garber, et. al., reported that stress levels among pharmacy students were significantly higher compared to standard populations. Pressure to succeed is one of the strong predictor of perceived stress among students. Hundertmark, et. al., stated that students who generally exhibit a high general stress levels in medical school are subjected to stressors such as time pressure, participant characteristics, teacher-role demands and study requirement.

To illicit the nature of high failure rate of students in the MTFQ modality examination, a focus group approach consisting of experts in the area of Medical Education, Cognitive Science, Knowledge Engineer Medical Expert, Educational Pedagogy and Clinical Psychologist Specialist were utilized. From the interview with Clinical Psychologist a Cause and Effect Chain analysis was formulated.

TRIZ-based Hybrid Methodology

Students' ability to perform across modalities was studied based on targeted student groups. Initial analysis revealed that students under performed in MTFQ modality examinations. Further to this the focus group session highlighted that stress was perceived as a key factor in students' inability to perform to their fullest potential. Interviews with students revealed that, not being prepared and being overwhelmed by diverse assessment needs were the stressors that affected their performance.

One of the key findings was that students tend to lack the ability to map their level of knowledge mastery into a successful answering strategy. Upon discussions with students who did well in the examination, it became apparent that a strategy to balance a risk taking attitude with an adequate field knowledge mastery was the key factor. Although the beneficial aspect of MTFQ compared to other modalities has not been extensively studied, Karimi and Manteufel showed that electronic administration of True/False multiple choice questions helps in measuring and reinforcing the understanding of fundamental concepts in Thermal Science course [START_REF] Karimi | Use of True-False or Multiple Choice Questions in Measuring and Improving Student Knowledge of Fundamental Concepts in Thermal Science Class[END_REF]. In the analysis of test items, the likelihood of right answer being correct can also be easily mapped to an answering strategy. The mapping of False statement into an answering strategy required additional cognitive loads owing to its added element of risk. As a problem modelling step, the main useful function of the MTFQ modality is presented in Figure 1. Although the initial model formulated the examination modality, with components such as Stem, Option, Answer, Distractor, Penalty, it became evident that a cognitive process modelling was crucial in highlighting variations in quality of assessments (see Table 2). We then came up with the perceptual cognitive mapping as shown in Figure 2 which took into considerations the lessons learnt in the TRIZ-based knowledge representation stage for solving such a complex model.

Function Modelling

Fig. 3. Function Analysis of Answer Strategy

The heuristic models (Figure 2 and 3) highlighted the underlying cause together with the interdependencies of the elements concerned. It allowed a visualization of observed effects via a graphical way. Based on this model, the cause for the high failure rate among preclinical students in MTFQ modality examination was evaluated. In using self-directed learning method, the cognitive loads of students were observed to be much higher when they identify a False statement, as compared to identifying a True statement. Awareness of a factual knowledge as evidence is sufficient to allow student to pinpoint True statements, where else False statements is based on "being convinced to the best of one's knowledge". Gathering factual knowledge as evidence for True statements requires less cognitive load on students. As a result, identifying of modalities requiring the False statement is a likely cause that posed as an added stressor. There was a need to investigate further if the negative question together with a need to context switching was the main cause for the high failure rates. TRIZ was thereby used as knowledge modelling framework for formulating these challenge scenarios.

Engineering Contradictions

Based on the initial analysis, the following engineering system was formulated. IF MTFQ is used, THEN learner knowledge is tested comprehensively BUT learners may experience high stress or pressure to perform. The improving parameter was selected as "productive" indicating the enabling level of learners' to attempt MTFQ in a productive manner. Meanwhile the worsening parameter was selected as "Stress or Pressure", which indicates the learners feeling of stress level while attempting the MTFQ.

The Inventive principles then provided insights in the modelling of MTFQ assessments by suggesting intuitive strategic directions. Based on these directions we have formulated the possible approaches as illustrated in Table 3. Table 3. Engineering Contradiction based on MTFQ modality used in examination with considering the improving parameter as Productive and the worsening parameter as Stress to the Learners was considered and the possible approaches postulated.

Inventive Principle Possible approach

Preliminary Action Prepare the student beforehand on the usage of the examination modality. This approach was in practise by the instructors and was also recommended by resolving this Engineering Contradiction.

Phase Transitions

To introduce interventions so that stressors are systematically harmonised so that the impact of the stressors will be neutralised.

Curvature

Students to apply various strategy while attempting the exam modality to simulate the sense of circularity (revisiting the questions based on certain algorithm). These strategies can be inculcated to the students to do.

Physical Contraditions

Finally, in utilizing Physical Contradiction, a contradictory analysis as a deep model of inventive solution (Table 4) was acquired. Table 4 highlights the reasoning strategies based on the three inventive principles identified via Physical Contradiction.

Table 4. Based on the recommendation from Engineering and Physical contradictions, an evaluation was carried out to determine the effectiveness of the proposed strategy. We next contrasted the performance of students before and after the intervention.

Inventive Principle Recommendation on Remodelling

Segmentation Need to structure questions or groups (segments) for reduced stress with a quicker answering strategy. This approach relates particularly to students deciding on which questions to answer first, and they mark questions for a second round analysis. In this context, training could be provided prior to the exams on how to segment the questions based on "ability to respond" Homogeneity Use the same medium as interface for a more focused answering strategy for students (stress reduced). We explore the possibility of using the same question form, but as a stress reducer, students only identify True statements. They are not required to ascertain the truth value of distractors.

Equipotentiality

Reduce the need for learners to determine the truth value of every statement. Identifying True statements is considered adequate.

3

Insights from the TRIZ-based models Figure 4 shows a sudden increase in passing rate in MTFQ modality examination among preclinical students in MDP10108, MDP10408 and MDP10507 courses after March 2020 (indicated by the vertical downward black arrow in Figure 4). The COVID-19 pandemic movement control order (MCO) was imposed in March 2020. The difference in the assessment of MTFQ pre and post pandemic (Table 5 Type A vs. Type B) has been mainly in the use of eLEAP platform. A MTFQ consist of a stem and five options. The author of the MTFQ decides an option to be True or False in any sequence order. Therefore, any number of options within 0 to 5 can be True or False. Prior to MCO, paper based assessment of MTFQ required a student to indicate the choice of option, which can be True, False or don't know (omit) by using an optical mark reader (OMR) sheet. Upon completing, the OMR is then scored using SmartScan software. One mark is awarded for correct answers while an incorrect answer is penalized by deducting one mark. An omitted option does not carry any value. Therefore, this enables a maximum mark awarded for a MTFQ to be 5 marks and the minimum mark is zero. The minimum marks are normalised to zero in order not to carry forward negative marks to the next question. During the pandemic, F2F interaction has been minimised and remote learning is engaged actively. The MTFQ is then replicated via eLEAP (learning management system). The MTFQ still has a stem and five options and any number of options within 0 to 5 can be True or False. The only difference is the choice of answers selected by the students. The students are required only to identify True options and key in their selection online. The marks for each question varies depending on the number of True options. The different marking scheme is depicted in Table 5.

Discussion

TRIZ-based models enabled us to tackle the aged problem in the field of medical education assessment. The modality of MTFQ has a high fatality rate. Applying problem solving tools available in TRIZ allowed us to deduce a solution to the pressing problem.

Stress was identified has one of the causes of this problem together with some cognitive and technical aspects. Function Analysis indicated the elements that may be influencing the goal of achieving high productivity among the learners. Engineering contradiction of "IF MTFQ is used, THEN learner knowledge is tested comprehensively BUT learners may experience high stress or pressure to perform" led us to deduce "productivity" as improving parameter while the worsening parameter was attributed to "stress". This in return enabled us to gain inventive principles such as preliminary action and curvature. Preparing learners prior to assessment may provide high productivity. Whereas learners can be coached to use various strategy mimicking a sense of circulatory such as revisiting questions based on refined algorithm. Through the use of physical contradiction, the inventive principles such as segmentation, homogeneity and equipotentiality came into light. Segmenting questions on the ability to respond is an example of this invention. As for equipotentiality, identifying only True statements instead of True and False can be attributed. The last inventive principle homogeneity has the ability to minimize stress through the application reducing the cognitive load. Learners are required to seek True statement only and this may contribute a homogenous thought process while attempting MTFQ.

Conclusion

TRIZ-based models which has been adapted for engineering domains has been shown in this paper to serve as a guide to move solution towards an ideal pathway through its heuristic modelling. The tools used in this project were incrementally improved and suited for the context of the discipline in query. This shows that TRIZ has the ability to produce a customized solution. TRIZ has act as a catalyst for remodeling of an ill structured multi-disciplinary real-world problem, with the goal of moving towards an ideal solution.

The exploration has demonstrated the potential use of TRIZ tools as aid for knowledge elicitation to help in modelling complex problems. TRIZ-based models can be used in enabling a structural modelling of future medical examination modality. The pandemic situation has turned out to be a blessing in disguise as it provided an opportunity for a methodical research/inquiry into the long-standing problem. Future studies may scrutinize the currently used model of assessment in post pandemic situation when F2F interaction is applicable. This will allow a comparison of pre and post using the current model of assessment.

The evaluation carried out revealed that the TRIZ based partial solutions were in fact workable. The preliminary findings demonstrated that future assessments can be formulated to serve as an ideal examination modality able to minimize stress effectively. Though interesting directions have been highlighted by the heuristic models discovered in this paper further research would be needed to test out and validate this hypothetical finding.

Fig. 1 .

 1 Fig. 1. Function model.

Fig. 2 .

 2 Fig. 2. Cause and Effect Chain Analysis

Fig 4 .

 4 Fig 4. The clustered bar chart shows the result in % for passing rate in MTFQ modality examination among preclinical students for 3 different courses, namely MDP10108, MDP10408 and MDP10507. The vertical downward black arrow indicates the beginning of the COVID-19 Pandemic, where the implementation of online examination via the eLEAP platform.

Table 1 .

 1 Overall concept methodology of the project.

	Research Methodology	Tools
	Review of Related Works	Review covered areas of Single Answers vs
		Multiple True False modes of assessments
		and Study of stressors in medical education.
	Interview with Domain Expert	CECA was used as a visual tool to generate
		and test hypothesis on the pathways to
		solve problem.
	Problem Modelling based on Function Analy-	Function Model was used to model domain
	sis	knowledge based on focus group discus-
		sions.
	Systems Analysis as a process to	Engineering Contradiction as a knowledge-
	formulate inventive problem solving model	based approach was used to identify direc-
		tions.
	Contradictory Analysis as a deep knowledge	Physical Contractions then served as an in-
	model of inventive solution	strument for deepening inquiry.
	Evaluation of Hypothesis	Review partial solutions was performed
		with an engagement with stakeholders to
		qualitatively enhance visual domain models.
	Analysing Student Performance in Summative	MTFQ modality examination component
	Assessment	was analysed to look for emerging patterns.

Table 2 :

 2 Preliminary Component Analysis.

	Components	System	Product	Super system (Cognitive model)
	Items	Question Stem	Learner	Knowledge-level indicator
		Option		Stress level indicator
		Answer		Fear of Wrong Answer
		Distractor		Willingness to take risk
		Penalty		Modality
		Medium		True/False decision

Table 5 :

 5 The table shows the description of a question with the respective answer given in Answer Column (shaded). Type A is the pre pandemic version (paper based assessment F2F) while type B is the post pandemic (via eLEAP online assessment). Student responses 1-4 are hypothetical answers from 4 different students. The results row shows the marks awarded for all the situation arising from SR-1 to SR-4.

	A: The following	Answer	SR-1	SR-2	SR-3	SR-4
	colours can be
	found in the rain-
	bow,
	A. blue	T	T	T	T	T
	B. green	T	T	T	T	T
	C. black	F	F	F	T	F
	D. brown	F	F	T	T	F
	E. red	T	F	F	F
	*RESULTS:	5	3	2	0	4
	* penalty for wrong answer (minus 1)
	SR -student response
					T	T
	*RESULTS:	5	3.33	3.33	1.66	0
	* penalty for wrong answer (minus depends on number of correct options), in this example it is 1.66 %
	SR -student response

B:The following colours can be found in the rainbow,AnswerSR 1 SR 2 SR 3 SR 4 A. blue T T T T B. green T T T T T C. black T T T D. brown T T E. red T T

Acknowledgments. The authors wish to thank Centre for Applied Learning and Multimedia, Universiti Malaysia Sarawak for the eLEAP support for this project.


T Lauvaux
email: lauvaux@meteo.psu.edu

B Gioli

C Sarrat

P J Rayner

P Ciais

F Chevallier

J Noilhan

F Miglietta

Y Brunet

E Ceschia

H Dolman

J A Elbers

C Gerbig

R Hutjes

N Jarosz

D Legain

M Uliasz

Bridging the gap between atmospheric concentrations and local ecosystem measurements

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This paper presents the first direct comparison of regional CO 2 fluxes estimated by inversion of atmospheric concentration data with fluxes measured by towers and aircraft. All measurements were made in a 300×300km domain in southwest France in 2005. Concentrations were measured on two short towers while fluxes were measured on 5 towers and 27 aircraft transects. The inversion produces a better fit than the prior estimate to the measured fluxes, capturing both the temporal evolution and behaviour of different ecosystems.

Additionally, the final estimate is most improved where the theoretical error reduction is highest. Results suggest that atmospheric inversion is a reliable tool for estimating regional CO 2 fluxes provided the components are verified.

D R A F T

June 11, 2009, 10:35am D R A F T

Introduction

Atmospheric inversions of CO 2 surface sources have played a key role in quantifying large-scale sources and sinks of CO 2 [e.g. [START_REF] Tans | Observational constraints on the global atmospheric CO 2 budget[END_REF]Gurney et al., 2002;[START_REF] Baker | Transcom 3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO 2 fluxes, 1988-2003[END_REF]. There are no direct measurements of CO 2 flux at these scales so the information cannot be verified. This paper attempts such a verification. We immediately face a problem of scale since we need sufficiently dense flux measurements to obtain spatial estimates comparable with the atmospheric inversions. During the CarboEurope Regional Experiment Strategy (CERES) in Southern France [Dolman et al., 2006], CO 2 fluxes were measured locally by the eddy covariance technique at five sites chosen to represent regional ecosystem types and also spatially by aircraft flying just above the surface. In addition, two towers measured continuously CO 2 concentrations. Eddy-flux measurements are completely independent of the inversion and are kept as validation data for the inverse fluxes. Inverse fluxes are calculated at 8km resolution over 6-day periods using hourly CO 2 measurements and high-resolution transport modelling. The temporal resolution is a compromise due to the lack of data (only two towers) but still uses the information from hourly concentrations. Sarrat et al. [2007b] and Lauvaux et al. [2008b] demonstrated the capability of the model to assimilate such observations.

The outline of the paper is as follows: In section 2 we briefly describe the tools and datasets underlying the study. Section 3 describes the major results while Section 4 considers some implications and summarises the results.

Inverse system and independent flux measurements

D R A F T June 11, 2009, 10:35am D R A F T X -5
The study period consists of 18 days in 2005 divided into 3 intensive observing periods, IOP-1 (May 24-29), IOP-2 (May 30-June 4) and IOP-3 (June 5-10). We estimate mean daytime fluxes for each IOP at 8×8km resolution (between 8am and 8pm). Hourly concentrations were measured on two towers throughout the period, at Biscarosse, located on the Atlantic coast at 50m height on a 70m hill, and Marmande, inland, at a height of 20m in an agricultural region (fig. 1). Influence functions of these two towers, describing the relation between surface fluxes and concentrations, were calculated using the non hydrostatic atmospheric model Meso-NH [START_REF] Lafore | The Meso-NH atmospheric simulation system. Part I: adiabatic formulation and control simulations[END_REF] coupled to the Lagrangian model LPDM [START_REF] Uliasz | Lagrangian particle modeling in mesoscale applications[END_REF]. Meso-NH was run at 8km resolution with 65 levels describing the with the ISBA-A-gs land surface model [START_REF] Calvet | An interactive vegetation SVAT model tested against data from six contrasting sites[END_REF]] at 8km resolution, forced by the SAFRAN meteorological analyses [START_REF] Durand | A meteorological estimation of relevant parameters for snow models[END_REF]. Concentration boundary conditions from the inversion come from a run of the LMDZ global model [START_REF] Sadourny | January and July performance of the LMD general circulation model in New perspectives in Climate Modeling[END_REF]. Boundary conditions are included in the inversion but have little impact [Lauvaux et al., 2008b].

We estimated the magnitudes and structures of the observation error covariance matrix by comparing direct simulations with atmospheric measurements [Lauvaux et al., 2008b] and their spatial structure from ensemble analyses [Lauvaux et al., 2008a]. forest) at 40m height to characterize the representative ecosystems of the flights over the region.

Results

We compare the errors of prior and posterior NEE from the airborne observations. The temporal resolution is limited to 6 days by the scarcity of concentration observations.

Figure 2 shows the 6-day mean corrected fluxes during the day for the forest ecosystems (deciduous and coniferous types), and agricultural ecosystems composed by winter crops (C 3 , mainly cereals) and summer crops (C 4 , mainly maize), with their associated standard deviations. The three IOP show significant trends in the averaged daytime NEE from both aircraft and ecosystem site flux data, corresponding to the rapid growth of summer crops starting in the IOP-3 (5 to 10 June). The trend in airborne NEE of increasing CO 2 uptake resembles the C 4 crop ecosystem flux measurements (from -3 µmol.m -2 .s -1 for IOP-1 to -8 µmol.m -2 .s -1 for IOP-2). The C 3 crop flux site NEE shows a decrease of the CO 2 uptake (from -11 to -8 µmol.m -2 .s-1).

Posterior NEE is closer to the airborne observations than is the prior for 9 out of 14 combinations of ecosystem and all the IOP shown in Fig. 2. Even though prior NEE is better for the forest than for the crops (only 2 to 4 µmol.m -2 .s-1 error, i.e. 50% of the absolute NEE), the posterior NEE still lies closer to the ecosystem observations. Posterior errors are 20% to 50% less than prior errors. The improvement occurs despite only having two concentration measurement series.

At 8km grid resolution, 14 inversion grid points lie on the two repeated aircraft transects (fig. 1). Fig. 3 The results suggest that when compared to direct flux measurements at comparable scales, this atmospheric inversion significantly improves the prior estimates; even where the prior is fairly good. Improvement occurs for both spatial structure and time evolution. This is true despite only having two concentration timeseries and despite the heterogeneity of the landscape.

One reason for the apparent success may be that the major components of the inversion system had been previously tested and the relevant uncertainties assigned accordingly.

Prior uncertainties were assigned by comparison with observations. The uncertainties on data were set by considering the mismatch between simulations and observations calculated by Sarrat et al. [2007a]; Lauvaux et al. [2008b] using the prior fluxes. This is a conservative choice since some of this mismatch comes from errors in the prior flux. We also accounted for some of the uncertainty in transport [Lauvaux et al., 2008a]. Finally Lauvaux et al. [2008b] has also shown that much of the domain is observable from the two measurement sites. Our results suggest that, if these conditions: reasonable prior, good transport and resonable signal are met the inversion is likely to produce meaningful results.

Finally, this study supports the use of aircraft flux measurements. Such measurements seem to be less constrained by representation problems than pointwise flux tower measurements. Although they cannot be used as a routine tool for monitoring regional fluxes, a combination of flux towers validating aircraft fluxes which in turn validate atmospheric inversions seems to provide the link between small and large scales required for quantifying and understanding regional carbon balances.

  atmospheric column up to 13km. The first vertical level represents the lowest 20m of the atmospheric column. The Lagrangian model LPDM is coupled offline to MesoNH, as described in Lauvaux et al. [2008b]. The typical surface flux area influencing the tower's concentration measurement extends 300km from the Atlantic Ocean to the Mediterranean coast (fig. 1, upper right corner, in red). The first guess fluxes were computed each hour

  For the prior D R A F T June 11, 2009, 10:35am D R A F T flux error covariances, we estimated the correlations of the differences between the ISBA simulation and measurements at 11 flux towers, from the method proposed by [Chevallier et al., 2006]. Only agricultural towers showed evidence of correlated flux errors which are introduced in the inversion setup as a correlation length of 50km for summer crops and winter crops. During the study period, 27 airborne transects were made to measure CO 2 surface fluxes over the same paths (fig. 1). Fluxes were measured with the eddy covariance technique by a Sky Arrow 650 ERA -Environmental Research Aircraft as described by Gioli et al. [2004]. Figure 1 illustrates the two airborne flux transects over the pine-forest ecosystem of Les Landes and the agricultural area of Marmande. The incoming photosynthetically active radiation (PAR) was used to extend the instantaneous aircraft measurements to 6-day daytime flux averages using the method from Gilmanov et al. [2007]. All flights were made at low altitude, ranging from 80 to 100m above the surface. During IOP-1 and IOP-3, the average measurement frequency is about 50 samples for each hour and 20 for IOP-2. Spatial averaging produces aggregated fluxes at about 4km scale and it is these that we compare with our inversions. Even though the inversion scale is larger (8km), they both remain much larger than the average agricultural plot scale (about 0.3km) which avoids representation error. For these larger scales, the corresponding ecosystem is the dominant type that covers at least 30% of the pixel. We selected five instrumented flux towers corresponding to the ecosystem types of the aircraft paths, Auradé and Lamasquère (cereals), Marmande and Saint Sardos (maize), at 2 to 6m height, and Le Bray (pine D R A F T June 11, 2009, 10:35am D R A F T X -7

  shows the corrected fraction ρ of the initial misfit (ρ = (ε corrected -D R A F T June 11, 2009, 10:35am D R A F T ε f irstguess )/ε f irstguess with ε = |N EE model -N EE observed | the model-data mismatch) at these locations. Negative values indicate an improvement. This metric penalizes cases with good priors such as the Les Landes forest (Western transect). The agricultural area (Eastern transect) shows better agreement for all locations (from 10 to 60% of reduction of the initial misfit). Both first guess and corrected flux estimates lie close to the flux measurements relative to the posterior uncertainty. We finally combine the spatial and temporal comparisons into an overall statistical measure of inversion performance. Fig 4 shows this statistical comparison for all the verification ecosystem NEE measurements and the inversion during daytime. Along the x-axis (from left to right), we show the prior misfit averaged over all the aircraft locations (with its standard deviation) and the same estimate after the inversion, and finally the two types of observations (aircraft and towers). The inversion decreases first guess misfit from 4 to 2 µmol.m -2 .s -1 (25% of the mean NEE) and reduces the NEE error by 15% over the area visible to the atmosphere (fig. 1). The error bars represent the mean square error of the prior/posterior divided by their respective uncertainty variances. This ratio tests the consistency of the inversion since it requires that, where the posterior error is smallest (i.e. the atmosphere provides most information) the match to independent flux measurements is most improved. The improvement in corrected fluxes is hence larger than the decrease of flux uncertainty suggesting that transport model error was slightly overestimated by the concentration data comparison. 4. Discussion and conclusions D R A F T June 11, 2009, 10:35am D R A F T X -9

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Averaged daytime NEE (in µmol.m -2 .s -1 ) from ISBA vegetation scheme

Acknowledgments. We wish to thank all participants in the CERES campaign for making their data freely available (http://carboregional.mediasfrance.org/campagne/index). This work was funded by the European Commission, Sixth Framework Programme, Contract No. GOCE- CT-2003-505572.

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