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Open access peer-reviewed chapter

# Biophysical and Economic Factors of Climate Change Impact Chain in the Agriculture Sector of ECOWAS

Written By

Calvin Atewamba and Edward R. Rhodes

Submitted: October 15th, 2018 Reviewed: July 8th, 2019 Published: January 8th, 2020

DOI: 10.5772/intechopen.84378

From the Edited Volume

## Environmental Health

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## Abstract

The chapter assesses key biophysical and economic factors of climate change impact chain in the agriculture sector of the Economic Community of West African States (ECOWAS), mainly within the decade following the launching of the Comprehensive Africa Agricultural Development Programme (CAADP) and Maputo Accord. This is done through a review of literature and analysis of data mainly from international databases. We find that land resources for agricultural production are substantial, but land degradation and land productivity are serious problems, particularly in the context of climate change. Although the region has experienced unprecedented growth, financing agricultural development is still an issue. Developing quality infrastructure and stimulating agricultural trade may provide a win-win strategy to build resilience to climate change and strengthen economic development. The economics of adaptation to climate change in the agricultural sector of ECOWAS has mainly focused on the magnitude of costs and returns on country-wide and technology-specific measures. There is a need, however, to integrate biophysical and economic factors of climate change impact chain in sound analytical frameworks to provide “multi-metric” considerations of non-monetary and nonmarket measures, risks, inequities, and behavioral biases in addressing climate change.

### Keywords

• agriculture
• ECOWAS
• Maputo accord
• climate change
• infrastructure
• climate finance

## 1. Introduction

Four major agroecological zones span the Economic Community of West African States (ECOWAS) region: these are the Sahelian, Sudan Savannah, Guinea Savannah, and Forest zone. At a broader level, ECOWAS has been grouped into a Gulf of Guinea zone and a Sudano-Sahelian zone based on geographical and climatic homogeneity [1]. All the Gulf of Guinea countries have shorelines with the Atlantic Ocean. The Sudano-Sahelian zone as a whole experiences a hotter and drier climate than the Gulf of Guinea zone. The countries in the former zone are Benin, Cote d’Ivoire, Ghana, Guinea, Guinea-Bissau, Liberia, Nigeria, Sierra Leone, and Togo. Burkina Faso, Cape Verde, the Gambia, Mali, Niger, and Senegal are in the latter zone. While the savannah spreads through both zones, the humid forest agroecology is mainly restricted to the Gulf of Guinea (Figure 1). The United Nations classified 11 of the 15 countries as least developed based on human resources, poverty level, and economic vulnerability. The exceptions were Ghana, Nigeria, Cote d’Ivoire, and Cape Verde [2]. However, because of its size, natural resources, and importance of agriculture in the economies, ECOWAS has a potential of contributing significantly to world trade, food security, and carbon storage.

Agriculture is the key sector of ECOWAS economies and the one that supports nearly 60% of the region population. The Comprehensive Africa Agriculture Development Programme (CAADP) and the declaration on agriculture and food security by the African Union commonly known as the “Maputo Accord” of 2003 promoted investment for the expansion of the area under sustainable land and water management, increased food supply and agricultural research, and technology dissemination in sub-Saharan Africa and the adoption of a policy of allocating at least 10% of annual national budgets to agriculture and attainment of 6% annual growth in the agriculture sector. The achievement of these goals is under threat from climate change, bearing in mind that the vulnerability of countries in ECOWAS to climate change is among the highest in the world [4]. Therefore, a critical challenge facing the region is how to feed an expected population of around 600 million by 2050 while simultaneously reducing and responding to climate change. There is a growing number of studies analyzing how agricultural production and commodity markets need to be adjusted to promote interregional balance in agricultural production and food security in response to climate change [5, 6, 7, 8, 9]. However, the uncertainties with regard to climate change impacts on agriculture remain considerable, and climate change impacts on food security are even less clear. The development of appropriate adaptation and mitigation measures to respond to or combat climate change is dependent on the knowledge of the climate change impacts as well as the nature and trends of the climate change impact chain factors.

The objective of this chapter is to broadly assess at the regional and zonal levels key biophysical and economic factors of the climate change impact chain in ECOWAS, especially within a decade after the CAADP and the Maputo Accord, and the economics of adaptation in the crop’s subsector. The assessment consists of an analysis of data from international databases and sources and information from other studies. Country national level data on land use, crop production, and yield for 2003 and 2013 are taken mainly from FAO and the World Bank databases and sources. Sums, means, ranges, and percentages are computed.

The remainder of the chapter is organized as follows. In Section 2, we underline the conceptual framework of climate change impact chain in the agriculture sector. Section 3 presents the biophysical factors, mainly land resources, land use, land degradation, and crop production. The economic factors are analyzed in Section 4, where we discussed how growth, inflation, infrastructure, and trade may shape the impacts of climate change on the agricultural sector of ECOWAS. In Section 5, we investigate the current knowledge on the economics of adaptation to climate change and raise the concern of integrating biophysical and economic factors to inform decision-making. Section 6 concludes and makes some remarks for further research.

## 2. Conceptual framework of climate change impact chain in the agriculture sector

The extent to which climate change affects the agriculture sector and food security depends on the flow of impacts from the environmental system to the economic system through biophysical and social systems that define the agriculture sector. The chain of climate change impacts can be conceptualized as follows (Figure 2).

Global warming manifests itself as increasing global mean air and ocean surface temperatures, which directly affect the local environmental system of agriculture, including climate, hydrology, and soil. Changes in the environmental system affect land use, crop yield, and production, which define the biophysical system of agriculture. The social system (population growth and distribution, human development) and the economic system (economic growth, trade, infrastructure) define the adaptive capacity of the agriculture sector to manage the changes in the biophysical system in order to guarantee food availability, access, and stability for the population. The resilience of these systems to the wave of climate-induced shocks defines the extent and the magnitude of climate change impact on the agriculture and food security. Indeed, these systems can either moderate or exacerbate the wave of climate-induced chocks on agriculture and food security. For example, if the biophysical system is vulnerable to climate-induced chocks, while the economic system is resilient, then the impact of climate change on agriculture and food security will be reduced.

Mapping the climate change impact chain in the agriculture sector may allow researchers and policy makers to understand the impacts of climate change and identify opportunities and challenges to reduce these impacts on agriculture and food security. In the following sections, we will investigate the biophysical and economic systems of the climate change impact chain in the agriculture sector of ECOWAS.

## 3. Biophysical factors: land resources, land use, land degradation, and crop production

### 3.1 Land resources, land use, and land degradation

The total surface area of ECOWAS is 504 million hectares made up of 207 million hectares in the Gulf of Guinea and 297 million hectares in the Sudano-Sahelian [10]. Total cultivable land area for the 15 ECOWAS countries is 196 million hectares out of which 130 million hectares were in the Gulf of Guinea and 66 million hectares in the Sudano-Sahelian zone [1]. Information on land use in 2003 and 2013 are shown in Table 1; some aspects were discussed by [11] who concluded that the situation is, in general, deteriorating.

Land useGulf of GuineaSudano-SahelianECOWASGulf of GuineaSudano-SahelianECOWAS
200320032003201320132013
Protected land (percentage of total land)
Mean4.87.45.718.513.316.8
Range0.7–11.42.3–11.60.7–11.62.4–27.14.4–24.22.4–27.1
Arable crop land (ha × 1000)
Total51,36728,37179,73852,43433,10685,540
Range270–35,00047–14,05047–35,000300–34,00055–16,80055–34,000
Permanent crop land (ha × 1000)
Total14,25732214,57915,68542716,112
Range130–64502–1452–6450165–65004–1504–6500
Arable + permanent crop land (percentage of total land)
Total31.89.718.7433.011.320.2
Range6.4–45.95.0–30.55.0–45.97.3–52.25.4–44.55.4–52.2
Forests (ha × 1000)
Total52,90322,33675,23947,71720,43668,153
Range
Forests (percentage of total land)
Total25.67.515.023.16.913.5
Range7.9–74.71.0–45.41.0–74.74.2–71.10.9–43.30.9–71.1
Carbon stocks in forests (million t)
Total5874834670852647706034
Range38–18413.7–3523.7–184120–18393.9–3363.9–1839

### Table 1.

Land use: areas under arable and permanent crops and carbon storage in forests in ECOWAS.

Source: Author’s calculations from [10, 11, 12].

The proportion of protected lands increased in both the Gulf of Guinea and Sudano-Sahelian zones probably indicating responsiveness by governments to global concerns for the preservation of natural resources. This contrasts with a decrease from 19.5 to 13.8% over the same period in protected lands in high-income countries [9, 13]. Lands under arable plus permanent crops were 31.8 and 9.7% in the Gulf of Guinea and Sudano-Sahelian zones, respectively, in 2003 and 33–11% in 2013. Land under arable crops increased to a much greater extent in the Sudano-Sahelian than the Gulf of Guinea. Overall, land under arable crops in ECOWAS increased by 7.3%. Area under permanent crops increased more in the Sudano-Sahelian than in the Gulf of Guinea, with an average increase of 10.5% for ECOWAS. Arable land plus permanent crop lands as a proportion of total land was almost the same in 2003 and in 2013 in the Gulf of Guinea. In the Sudano-Sahelian, there was a small increase from 9.7 in 2003 to 11.3% in 2013. For ECOWAS as a whole, it was 18.7% in 2003 and 20.2% in 2013.

These findings suggest a high proportion of land reserves for agricultural production and variability between zones. However, it would have been more meaningful to express arable plus permanent croplands as a percentage of cultivable land, but the definition of cultivable land lacks clarity. According to [1] “cultivable area is an area of land potentially fit for cultivation. This term may or may not include part or all of the forests and rangeland. Assumptions made in assessing cultivable land vary from country to country. In this (FAO) survey, national figures have been used whenever available, despite possible large discrepancies in computation methods.” Research is therefore needed on reliably estimating cultivable land to facilitate the assessment of key factors controlling climate change impacts.

Area under forests declined at the rate of 9.8 and 8.5% in the Gulf of Guinea and Sudano-Sahelian, respectively. Overall, there was a 9.4% decline in area under forests in ECOWAS over 10 years (Table 1). The decline in the Sudano-Sahelian zone may, however, not be uniform because the conversion of biomass into forest has taken place in the Sudano-Sahelian zone [15]. The increase in arable area and decrease in area under forests in ECOWAS associated with the release of carbon to the atmosphere would contribute to land degradation.

The estimated carbon stocks in forests of ECOWAS (Table 1) were substantial (6708 million t in 2003 and 6034 million t in 2013) but significantly greater in the Gulf of Guinea, where forests predominate, than the Sudano-Sahelian. The variation of carbon stocks with agroecosystems as measured in the field and laboratory [16] showed that for mangrove ecosystems, roots and soil together accounted for about 86% of the total ecosystem carbon stocks (463 and 1382 Mg C ha−1 in the low mangroves of semiarid Senegal and in the tall mangroves of humid Liberia, respectively).

ECOWAS countries have experienced significant land degradation [15, 17]. Based on land area data of the World Bank [10, 14] and areas of degraded land [17], it is estimated that up to 644,000 km2 (31%) of lands in the Gulf of Guinea and 1,124,000 km2 (38%) of lands in the Sudano-Sahelian zone and 1,768,000 km2 (35%) of lands in ECOWAS were severely to very severely degraded by 2000. Nkonya et al. [18], however, reported a lower but still important rate of 19% of lands excluding deserts for Niger. The primary causes of land degradation in ECOWAS are deforestation, agriculture, conversion of grasslands to croplands, and overgrazing [18, 19]. Deforestation in ECOWAS is associated with slash and burn agriculture as well as with fuelwood, charcoal, and timber production to meet basic livelihood needs of small-holder farmers and boost incomes of commercial enterprises. Moussa et al. [19] estimate that more than 60% of carbon dioxide emission in Africa is due to deforestation and land degradation. Land reclamation to combat degradation is therefore a climate change adaptation option requiring financing by governments and their international development partners.

### 3.2 Crop production

The FAO database on crop production is available on the basis of country and not on farming systems or agroecological zones (AEZ). Nevertheless, it is well known that millet and sorghum are the traditional cereals of the Sudano-Sahelian, and maize, the roots and tubers, and tree crops are mainly cultivated in the Gulf of Guinea. With the development and release of new varieties of crops and changing climate, the distribution of these crops across ECOWAS is changing. Rice cultivation is becoming ubiquitous throughout the region as the urban population and demand for rice increase.

The production and yield of the major food and cash crops—rice, maize, millet and sorghum grains, cassava and yam tubers, groundnut (unshelled), cotton lint, coffee green berries, cocoa beans and palm oil—for the Gulf of Guinea and the Sudano-Sahelian zones are shown in Tables 2, 3, 4; along these lines:

Production (×1000 t)Yield (t ha−1)
2003201320032013
Gulf of Guinea591211,7391.481.73
Range54.2–3116209.7–48230.83–2.311.25–3.30
Sudano-Sahelian134428632.352.91
Range20.5–938.269.7–19781.77–3.101.05–6.28
ECOWAS725614,6021.591.88
Maize
Gulf of Guinea887813,5771.501.44
Range16–52037.3–84231.00–2.240.49–2.15
Sudano-Sahelian156935041.591.97
Range2.2–665.55.8–16360.38–2.280.18–2.59
ECOWAS10,44717,0811.511.52
Millet
Gulf of Guinea676514741.320.72
Range10–626018.1–9100.65–1.380.61–1.29
Sudano-Sahelian593864640.590.58
Range120.3–274593.8–29220.48–1.090.41–0.94
ECOWAS12,70379380.840.60
Sorghum
Gulf of Guinea876860791.130.98
Range10–801626.9–53000.55–1.160.67–1.35
Sudano-Sahelian311547920.650.70
Range30.1–161030.4–18800.27–1.130.37–1.11
ECOWAS11,88310,8710.950.83

### Table 2.

Cereal production in ECOWAS.

Source:[11, 13].

Production (×1000 t)Yield (t ha−1)
2003201320032013
Cassava
Gulf of Guinea55,64776,21510.288.37
Range38–36,30423–47,4075.86–15.23.52–18.27
Sudano-Sahelian3443846.869.75
Range3.4–181.74.1–156.12.17–17.901.36–19.97
ECOWAS55,99176,59910.258.37
Yam
Gulf of Guinea41,01752,19710.457.83
Range20.5–29,69721.5–35,6188.67–12.116.61–16.78
Sudano-Sahelian6717112.368.77
Range31–3579.2–91.612.01–12.805.86–20.63
ECOWAS41,08452,36810.457.83
Groundnut
Gulf of Guinea405636641.340.97
Range4.3–30376.5–24750.60–1.530.64–1.24
Sudano-Sahelian131619790.770.78
Range92.9–440.70.28–677.5049–0.890.49–1.38
ECOWAS537256431.130.89

### Table 3.

Cassava, yam, and groundnut production in ECOWAS.

Source:[11, 13].

Production (×1000 t)Yield (t ha−1)
2003201320032013
Coffee green
Gulf of Guinea192.3172.60.370.21
Range0.06–140.00.07–103.70.2–1.70.14–2.48
Sudano-Sahelian0.0620.21
ECOWAS192.3172.70.76
Cocoa beans
Gulf of Guinea226326960.490.48
Range0.1–13520.12–14490.17–0.680.14–0.86
ECOWAS226326960.490.48
Cotton lint
Gulf of Guinea573368
Range1.8–1721.4–133.5
Sudano-Sahelian447422
Range0.18–259.70.19–280
ECOWAS1020790
Palm oil
Gulf of Guinea15281638
Range4.9–10226–880
Sudano-Sahelian917
Range2.5–63–13.7
ECOWAS15371655

### Table 4.

Perennial and cash crop production in ECOWAS.

Source:authors calculations from [11, 13].

#### 3.2.1 Annual crops: cereals

The production and yield of rice in the Gulf of Guinea zone increased by 99 and 17%, respectively; for the Sudano-Sahelian zone, the corresponding values were 113 and 24%. The production of maize in the Gulf of Guinea zone rose by 53%, but yield declined by 4%. The production and yield of millet in the Gulf of Guinea zone declined by 78 and 45%, respectively. In the Sudano-Sahelian, zone production increased by 9%, but yield declined by 3%. For sorghum, production and yield in the Gulf of Guinea decreased by 31 and 14%, respectively; contrary to this, production and yield increased by 54 and 8%, respectively, in the Sudano-Sahelian zone.

#### 3.2.2 Annual crops: roots and tubers and groundnut

The production of cassava in the Gulf of Guinea zone increased by 37%, but yield declined by 19%. In the Sudano-Sahelian zone, production and yield increased by 12 and 42%, respectively; this was a desirable case of yield increasing substantially over time. The production of yam in the Gulf of Guinea increased by 27%, but yield decreased by 25%. Similarly, the production in the Sudano-Sahelian zone increased by 157%, but yield declined by 29%. The large increase in yam production in the Sudano-Sahelian may indicate evolving farming systems because yam was traditionally a major crop in the humid areas of ECOWAS. In the Gulf of Guinea, production and yield of groundnut declined by 10 and 28%, respectively. In the Sudano-Sahelian, production and yield increased by 50 and 1%, respectively.

#### 3.2.3 Zonal effects on crop production and yield

Crop production was higher in the Gulf of Guinea than the Sudano-Sahelian zone, with Nigeria being the highest producer in ECOWAS of rice, maize, sorghum, cassava, yam, and groundnut in both 2003 and 2013. World Bank [20] also reported higher crop production in the humid and subhumid AEZs than the semiarid zone. The greater proportion of the humid and subhumid zones is within the Gulf of Guinea zone, and this may explain in part why production of the major crops was higher in this zone. The average yield of rice, maize, and yam in the Sudano-Sahelian zone was, however, higher than the average yield of these crops in the Gulf of Guinea zone in both years. Thus, the highest yield of rice in 2003 and 2013 was reported for Niger, and that of maize in 2003 was for Senegal, and in 2013 it was for Mali. In both years, the highest yield of cassava was reported for Niger and that of yam in both years for Mali. These findings are relevant in exploring how climate change may impact production and productivity differently, in various parts of ECOWAS, and how this knowledge can be exploited for improved food security and poverty alleviation.

#### 3.2.4 Changes in crop production and yield over time

The production of rice, maize, cassava, yam, and groundnut increased between 2003 and 2013, but that of millet and sorghum decreased. In contrast to this positive change in production, yields of millet, sorghum, cassava, yam, and groundnut decreased, and although those of rice and maize increased slightly in ECOWAS as a whole, yields were low and well below their potentials. Increases in crop production in ECOWAS are generally more closely related to the area harvested than to yield per unit area [22]. Lipton et al. [23] reported yields of 1.01 t ha−1 for rice, 0.78 t ha−1 for maize, 0.56 t ha−1 for millet, 0.76 t ha−1 for sorghum, and 7.63 t ha−1 for cassava in Western Africa for 1961–1963. These levels, compared to those shown in Tables 2 and 3, indicate only modest increases over four to five decades from a very low baseline. Thus, the evidence is that while crop production increased, the boosting of crop yields (productivity), a major concern of CAADP and the Maputo Accord did not take place during the period under review. This finding should be of serious concern given that the Consultative Group on International Agricultural Research (CGIAR) centers in collaboration with the National Agricultural Research and Extension Systems (NARES) have developed and released high-yielding, pest- and disease-resistant crop varieties with associated improved crop and soil management practices over the past three to four decades and increase in crop yields is recognized as a major step toward poverty reduction and food security [23]. The impacts of climate change on agriculture have reinforced the need for achievement and maintenance of high crop yields as an adaptation measure both by small-scale and large-scale investors.

### 3.3 Perennial and cash crops

Data for coffee, cocoa, and palm oil (from oil palm) were available almost exclusively for the Gulf of Guinea zone where they are mainly cultivated. For coffee, in the Gulf of Guinea zone, production and yield decreased by 10 and 45%, respectively. Production of cocoa increased by 19%, while yield decreased by 3%. Cote d’Ivoire in 2003 and 2013 was the highest producer in ECOWAS of coffee green berries and cocoa beans. Like for annual crops, yields of cocoa and coffee were well below potentials, and their improvement should be a sector development priority for governments. Production of palm oil increased by 7% in the Gulf of Guinea and 96% in the Sudano-Sahelian zone (data only for Gambia and Senegal), but the production of cotton lint in the Gulf of Guinea and Sudano-Sahelian zone declined by 36 and 6%, respectively. This contrasts with the 7.3% per annum increase in cotton production between 1980 and 2006 in West Africa reported by [21]. Mali in 2003 and Burkina Faso in 2013 were the highest producers of cotton lint in ECOWAS. Data were not available on yield of palm oil and cotton.

## 4. Economic factors: GDP, inflation, infrastructure, and trade

The vulnerability of the ECOWAS agricultural system to climate change depends partly on certain economic factors such as income, price level, labor productivity, transportation, communication, innovation, and trade, which define ECOWAS’ adaptive capacity to external shocks, including climate change. The greater the adaptive capacity of ECOWAS, the lower its vulnerability to climate change, particularly in the agricultural sector.

### 4.1 Growth, inflation, and capital formation

After several years of strong economic growth, ECOWAS faced a small increase in 2016 of 0.5%. It rebounded in 2017 to 2.5% and was projected to 3.8% in 2018 and 3.9% in 2019. Countries’ performance varied, but because Nigeria, Cote d’Ivoire, Ghana, and Senegal contribute to about 90% of the regional gross domestic product (GDP), their patterns largely shape regional ones. In 2003, agriculture was the dominant sector in ECOWAS (about 40% of GDP), but services contributed most to GDP in Liberia and Sierra Leone soon after the end of their civil wars which devastated the agriculture sector; however, agriculture remains dominant in 2013 [24].

GDP per capita increased by 31.3% in ECOWAS, 34.8% in the Gulf of Guinea, and 26.9% in Sudano-Sahelian between 2003 and 2013 (Table 5), indicating an increase in standard of living. Furthermore, consumer prices almost double during the same period, threatening the positive effect of the increased income. Changes in the productive capacity of ECOWAS captured by the gross capital formation represented a larger share of the GDP in 2013 than 2003. The same trend is observed in the Gulf of Guinea and Sudano-Sahelian zones. Agricultural labor productivity increased by 22% between 2003 and 2013 in ECOWAS, while it decreased by 18% in Sudano-Sahelian zone. This may be explained partly by an increase in fertilizer consumption in ECOWAS and in both agroecological zones (Table 5).

Zone/regionGDP per capita (constant 2010 US$)Consumer price index (2010 = 100)Gross capital formation (percentage of GDP)Agriculture, value added per worker (constant 2010 US$)Fertilizer consumption (kilograms per hectare of arable land)
2003201320032013200320132003201320032013
Gulf of Guinea
Total144.3165.2
Mean736.0992.164.7122.59.1–23.87.2–27.81030.91584.78.616.3
Range271.0–1426.9383.1–2475.940.8–83.6108.2–156.4420.0–2445.3521.5–5041.10.8–29.32.9–37.2
Sudano-Sahelian
Total90.2165.5
Mean870.11104.080.7108.41215.3996.97.812.1
Range335.7–2310.5373.7–3389.967.7–85.2105.6–115.510.0–22.317.8–36.2544.7–1960.8470.5–1298.50.3–10.90.4–31.5
ECOWAS789.61036.972.1116.9234.5330.71107.71349.68.214.4

### Table 5.

Growth, inflation, and capital formation.

Source:Authors calculations from the World Bank Open Data [23].

Financing adaptation and mitigation are an important component of building resilient of the agricultural sector to climate change in ECOWAS. As observed in the previous paragraph, increasing income per capita, investment, and labor productivity are an indication that further economic efficiency in production may be realized in ECOWAS to support the financing of mitigation and adaptation efforts for climate change. However, higher consumer prices represent a significant challenge that may offset the positive effect of an improved efficiency in production for climate finance. Furthermore climate change compounds with other pressing socioeconomic development challenges such as education, sanitation, health and infrastructure, resulting to underinvestment in agriculture in ECOWAS. As reported by AfDB [25], the agriculture sector in ECOWAS suffers from chronic underinvestment. Only Burkina Faso, Mali, Niger, and Senegal have so far raised public expenditure to 10% of GDP, the target fixed by the Maputo Declaration in 2003. The Gambia, Ghana, and Togo are on the threshold of reaching this target. Nigeria devotes 6% of GDP to agriculture and the remaining ECOWAS countries less than 5%. This is not surprising because in the presence of limited resources and a range of objectives, financing agricultural development issues such as climate change should involve trade-offs among multiple policy goals. Therefore, financing climate policies, programs, and plans in the agricultural sector of ECOWAS should be prioritized not only in terms of their ability to reduce the impact of climate change but also in terms of their ability to deliver some development outcomes.

### 4.2 Infrastructure development

Infrastructure development in ECOWAS can be analyzed in three key areas: communication, transport, and technology. The telecommunication priority is the development of a reliable and modern regional telecom broadband infrastructure including the INTELCOM II program, alternative broadband infrastructure, and submarine cables as well as the establishment of a single liberalized telecom market. By 2013, 11 coastal member states were connected to submarine cables with at least 1 new landing station, and the 3 landlocked countries (Burkina Faso, Mali, and Niger) now have at least 2 access routes to the submarine cables. This has substantially increased the percentage of people using the Internet (from 1.1% in 2003 to 9.9% in 2013) and number of subscriptions to mobile cellular (from 4 subscriptions in 2003 to 78.4 subscriptions in 2013 per 100 people). A similar trend is observed in Gulf of Guinea and Sudano-Sahelian zones.

The transport program in ECOWAS has overseen the implementation of multimodal transport infrastructure and policies to promote physical cohesion among member states and to facilitate the movement of persons, goods, and services within the community with special emphasis on increased access to island and landlocked countries. However, the transportation infrastructure is still underdeveloped and of poor quality. For example, the quality of port infrastructure was estimated at 3.9 on a scale of 7, the latter representing a well-developed and efficient infrastructure by international standards. Rail lines decreased by 72% between 2003 and 2013. This is mainly due to a sharp decrease of rail lines in the Gulf of Guinea zone (Table 6).

Zone/RegionIndividuals using the Internet (percentage of the population)Mobile cellular subscriptions (per 100 people)Trademark applications, totalQuality of port infrastructure, WEFaRail lines (total route-km)
2003201320032013200320132003201320032013
Gulf of Guinea
Total1313.024,888.04482.0639.0
Mean0.77.82.973.70.03.7
Range0.0–1.43.1–19.10.1–7.255.9–106.4627–686.014–19332.00.0–0.03.2–4.5977–3505.0639–639.0
Sodano-Sahelian
Total358.0406.00622.0
Mean1.613.15.885.40.04.1
Range0.2–4.31.15–37.50.7–11.638.0–119.925–298.0406.0–406.00.0–0.03.5–4.80.0–0.0622.0–622.0
ECOWAS1.19.94.078.41671.025,294.00.03.94482.01261.0

### Table 6.

Infrastructure development.

a: 1, extremely underdeveloped, to 7, well developed and efficient by international standards).

Source:Authors’ calculations from the World Bank Open Data [23].

ECOWAS countries still have a long way to go to reach the African Union’s target of devoting 1% of GDP to gross domestic expenditure on research and development (GERD). Mali comes closest (0.66% in 2010), followed by Senegal (0.54% in 2010), according to the UNESCO Science Report [25]. There is a lack of researchers in ECOWAS in general. AfDB [25] highlighted that only Senegal stands out, with 361 full-time equivalent (FTE) researchers per million population in 2010, while other countries, where data was available, have less than 60. However, the number of trademark applications, as an indicator of innovation, has increased substantially between 2003 and 2013 from 1671 to 25,294. Almost all trademark applications are from the Gulf of Guinea zone (99%).

Infrastructure development is an important means to build resilience to climate change, particularly in the agricultural sector, because it also delivers vital development outcomes. We should recognize that the availability and quality of infrastructure are never substitutes to agriculture-specific policies such as an increase in fertilizer use, irrigation, and improved seeds. However, inadequate infrastructure may be a significant constraint to growth and productivity. Indeed, recent literature indicates a significant positive link between infrastructure and agricultural productivity [26]. For example, transport infrastructure provides important connectivity with growing markets and also reduces input costs and transaction costs for producers and consumers, particularly in the context of climate change. Furthermore, information acquisition costs can represent a significant obstacle, for instance, when climate and weather data are costly or difficult to access. Improvement in communication infrastructure represents an opportunity to reduce information acquisition costs, thereby strengthening farmers’ responses to external shocks such as climate change.

Recent literature also recognizes that innovation (technological, managerial, and institutional) in agriculture is clearly an important response for effective and equitable adaptation to and mitigation of climate change. As underlined by Llanto [27], innovation can enhance technology adoption, may prevent or facilitate migration of production/population, enhance trade and aid, and increase efficiency of insurance and feasibility of inventories. More importantly, innovation will be the key in moving toward climate-smart agriculture.

ECOWAS has a huge potential for trade both in global and intra-regional terms mainly because of its large natural resource endowment, agricultural potential, and intra-regional complementarities. Trade (the sum of exports and imports of goods and services) was estimated at almost 65% of GDP in 2003 and 78% of the GDP in 2013, representing an increase of 13 points in 10 years. A similar trend is observed in Gulf of Guinea and Sudano-Sahelian zones. The export profile of ECOWAS shows little product diversity, with a heavy reliance on extractive products (e.g., petroleum, natural gas) and a few agricultural commodities (e.g., cocoa, rubber, cotton). Agricultural raw material exports measured as a share of merchandise exports decreased by 12 points between 2003 and 2013. The decrease is substantial in Sudano-Sahelian zone (20 points) and moderate in the Gulf of Guinea zone (5 points). However, food exports measured as a share of merchandise exports increased by 19 points in the Sudano-Sahelian zone and decreased by 15 points in the Gulf of Guinea zone (Table 7). This is an indication of an improvement in the industrialization of ECOWAS and/or building of adaptive capacity to environmental and economic shocks, such as climate change.

Zone/regionTrade (percentage of GDP)Agricultural raw material imports (percentage of merchandise imports)Agricultural raw material exports (percentage of merchandise exports)Food imports (percentage of merchandise imports)Food exports (percentage of merchandise exports)
2003201320032013200320132003201320032013
Gulf of Guinea
Total
Mean67.981.11.31.317.913.126.320.937.422.9
Range43.3–102.531.0–131.00.4–4.00.4–2.80.0–74.23.2–49.115.5–62.414.2–40.30.0–95.44.9–38.5
Sudano-Sahelian
Total
Mean60.472.92.01.329.49.828.127.732.551.3
Range30.7–98.861.7–95.30.7–4.30.4–2.63.3–79.50.0–44.418.0–37.612.1–37.36.4–85.98.0–92.0
ECOWAS64.977.81.71.323.611.627.224.034.935.8

### Table 7.

Source:authors calculations from the World Bank Open Data [23].

ECOWAS imports are more diversified, with a high share of industrialized products (e.g., refined petroleum, vehicles, ships, telecommunication equipment) and food products (e.g., rice, wheat). Agricultural raw material imports measured as a share of merchandise imports decreased slightly by 0.4 points between 2003 and 2013. The same trend is observed in Sudano-Sahelian and Gulf of Guinea zones. On the other hand, food imports measured as a share of merchandise imports decreased in ECOWAS (3.2 points), Sudano-Sahelian zone (0.4 points), and Gulf of Guinea zone (5.4 points) between 2003 and 2013. ECOWAS main trading partners are highly industrialized countries such as China, India, the USA, EU countries, and Brazil, which mainly buy raw materials and sell industrialized products from/to the region. Intra-regional trade takes place, but is mainly, unreported, informal and generally considered to be well below its potential [29].

## 5. Economics of adaptation to climate change in the agriculture sector

Recent literature on the impact of future climate change on West African crop yields showed a large dispersion of yield changes ranging from −50 to +90%, with the median yield loss near −11% [32]. The predicted impact is larger in Sudano-Sahelian region (−18% median response) than in the Gulf of Guinea (−13%). Roudier et al. [32] highlighted that the consistently negative impact of climate change results mainly from the temperature whose increase projected by climate models is much larger relative to precipitation change. As discussed in previous sections, the vulnerability of the biophysical system and the underdeveloped economic system of ECOWAS will exacerbate this impact on agriculture and food security. Economic analysis of adaptation in the agriculture sector of ECOWAS is still in its infancy state, and information even on costs benefit analysis of adaptation options in the agriculture sector of ECOWAS is scarce. Nevertheless, some valuable information on the magnitudes of costs and returns on a country-wide and technology-specific basis has emerged.

Butt et al. [33], through modeling studies, showed that for Mali, policy changes that result in reduction in soil productivity loss, cropland expansion, adoption of improved cultivars, and changes in trade patterns altogether, under climate change, showed an annual gain of $252 million in economic benefits as opposed to a$161 million loss without policy adjustment. Roudier et al. [32] examined the benefits of climate change adaptation in agriculture for Ghana when the whole adaptation resource envelope is spent on gradual expansion of irrigated land area from 2012 onwards. The assumed upfront investment cost of irrigation is $18,000 per ha, taking account of Ghana-specific cost estimates for recent and planned irrigation projects plus the need for complementary investment in water harvesting, etc. Under the general circulation model (GCM)/Special Report on Emissions Scenarios (SRES) of the IPCC modeling global wet scenario, the share of irrigated land rises gradually from less than 0.4 to 15% of the current total cultivated area. The resulting average annual factor productivity increase for agriculture as a whole is an additional 0.36% above baseline productivity growth. They also pointed out that this scenario can also be interpreted as representing other productivity-rising agricultural adaptation measures with a comparable yield impact per dollar spent. It is well known that technological adaptations such as adoption of high-yielding pest and disease-resistant varieties of climate-smart varieties of cassava can double crop yields even without the use of expensive inputs (and therefore positive returns), in the immediate term. On the other hand, adaptation options in the form of soil conservation practices such as contour ridges and agroforestry require investments to pay off over longer periods, which small-scale farmers cannot afford in the typical situation of lack of long-term credit facilities by commercial banks. Persons with precarious hold on the land, such as women and strangers, are particularly constrained to make such investments. Thus, World Bank [34] reported that while farmers in Nigeria who were dependent on leased and/or communal lands expressed implicit dislike for climate-smart agriculture (CSA)-related investments, the majority with freehold titles, particularly those with registered titles, expressed positive willingness-to-accept incentives to embrace CSA and combat land degradation [35]. The following examples illustrate the nature of the investments and returns in soil management adaptation options in ECOWAS: in the Sahel of ECOWAS, stone bunds associated with shallow pits, filled with compost or manure (Zai pits), requiring 30–50 t of stones ha−1 and costing$200 ha−1 and 150 person days of labor ha−1 for constructing the bunds on contours, have resulted in doubling of millet yields [36]. Bjorkemar [37] estimated the potential returns over 25 years from agroforestry, in a village in the Bombali District of Sierra Leone, as follows: $15,470,$135,812, $5,427,800, and$11,903,090 for dispersed interplanting, boundary planting, and woodlot and fruit orchard, respectively. A World Agroforestry Center study reported by [36] showed that farmer-managed natural regeneration raised millet yields from 150 to 500 kg ha−1 in Maradi, Niger, taking into consideration improvement in soil fertility, and increased supply of food, fodder, and firewood was at least a $56 ha−1 return each year. Analysis of the economics of adaptation to climate change is moving from a focus on efficiency, market solutions, and cost-benefit analysis of adaptation to include “multi-metric” considerations of non-monetary and nonmarket measures, risks, inequities, and behavioral biases and barriers and limits and consideration of ancillary benefits and costs for providing support to decision-makers [31]. An understanding of the controlling factors of climate change impact chain is useful as inputs to these kinds of analysis. A few studies on economics of adaptation to climate change in ECOWAS have reached such sophistication. Recently, Aklesso et al. [38] tried to integrate a number of biophysical and economic factors of climate change impact chain in order to analyze the potential of intra-regional trade in ECOWAS for increasing food availability in the context of climate change. Several models were integrated: a regional climate model to predict temperature and precipitations from 2004 to 2100 with two representative concentration pathways (RCPs); an econometric crop simulator to simulate crop yield under RCPs; a bioeconomic optimization model to predict agricultural land allocation and crop production under RCPs; and an intra-regional food trade module built from a classical transportation model to allocate food optimally from excess supply countries to excess demand countries. The authors showed that the climate-induced trade pattern in ECOWAS depends on the prevailing socioeconomic conditions during the century, and several countries may become dependent on food imports outside ECOWAS. However, doubling crop yields by 2050 and adjusting the ECOWAS common external tariffs could significantly reduce outside dependence. Although this study attempts to investigate the link between climate change and food security in ECOWAS, more research is needed to understand how the integration of factors of climate change impact chain could affect food security and promote sustainable agricultural development in ECOWAS. Advertisement ## 6. Conclusion This chapter assessed key biophysical and economic factors of the climate change impact chain and the economics of adaptation in the agricultural sector of ECOWAS. As in many developing regions, land for agricultural production in ECOWAS has increased at the expense of forest land. These changes vary, however, by agroecological zones. Furthermore, ECOWAS countries have experienced significant land degradation. The primary causes of land degradation are deforestation, agriculture, conversion of grasslands to croplands, and overgrazing. Cropping systems are generally related to agroecological zones; however, the release of new varieties of crops and changing climate is significantly changing the distribution of crops across ECOWAS. Crop production was higher in the Gulf of Guinea than the Sudano-Sahelian zone. This is partly explained by the high proportion of humid and subhumid zones within the Gulf of Guinea. Increases in crop production in ECOWAS are more often related to the area harvested than to yield per unit area, which is the major concern of CAADP and the Maputo Accord. The boost in crop productivity expected from CAADP and the Maputo Accord did not happen between 2003 and 2013. Increasing crop yields through agricultural intensification while reducing land degradation is critical to reduce the impact of climate change in the agricultural sector of ECOWAS. In recent years, ECOWAS has experienced an increase in income per capita, investment, and labor productivity, indicating that further economic efficiency in production may be realized. This may boost climate financing in the agricultural sector. However, further improvement in general production may not generate enough resources to address both climate change and other development challenges, particularly in the context of increasing prices. There is a need for policy makers to prioritize climate strategies that also have some development impacts. Infrastructure in ECOWAS is underdeveloped with poor quality. Although the availability and quality of infrastructure may never substitute for agriculture-specific policies such as an increase fertilizer use, irrigation, and improved seeds, infrastructure development can help build resilience to climate change. Indeed, infrastructure development provides important connectivity with growing markets and also reduces input, transaction, and information acquisition costs for farmers and other actors in the agricultural sector of ECOWAS. On the other hand, ECOWAS has a huge potential for trade both in global and intra-regional terms mainly because of its large natural resource endowment, agricultural potential, and intra-regional complementarities. However, intra-regional trade that takes place in ECOWAS is mainly informal and generally considered to be well below its potential. In the context of insufficient financial resources to support climate adaptation actions, stimulating trade appears as an appropriate measure to preserve food availability by allowing countries with excess food production to trade with food-deficit countries. Returns to adaptation to climate change in ECOWAS can vary widely depending on the technology with gains of up to$252 million in economic benefits compared to \$161 loss without policy adjustment in a country in the Sudano-Sahelian zone. The economics of adaptation to climate change in the agricultural sector of ECOWAS has focused so far on the magnitude of costs and returns on a country-wide and technology-specific measures. There is a need, however, for further research to integrate biophysical and economic factors of climate change impact chain in sound analytical frameworks to provide “multi-metric” considerations of non-monetary and nonmarket measures, risks, inequities, and behavioral biases in addressing climate change.

Although important results were obtained regarding the biophysical and economic opportunities and challenges for building the resilience of the agriculture sector of ECOWAS to climate change, our study presents some limitations. For example, a detailed year-to-year trend analysis from 2003 to 2013 is not done because of the wide scope of the study (mapping), and data are not available for some parameters for some countries, and some data are not available for the same years for all variables studied. In addition, the environmental and social factors that are not covered in the study are equally important in defining the climate change impact chain in the agricultural sectors. These issues will be addressed in further research.

## References

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6. 6. Nelson GC, Rosegrant M, Koo J, Robertson R, Sulser T, Zhu T, et al. Climate Change: Impact on Agriculture and Costs of Adaptation. Washington: International Food Policy Research Institute; 2009
7. 7. Jalloh A, Nelson G, Thomas T, Zougmore R, Roy-Macauley H. West African Agriculture and Climate Change. Washington: International Food Policy Research Institute; 2013
8. 8. Rhodes E, Jalloh A, Diouf A. Review of Research and Policies for Climate Change Adaptation in the Agriculture Sector in West Africa. Brighton: AfricaInteract, Institute of Development Studies; 2014
9. 9. Roudier P, Ducharne A, Feyen L. Climate change impacts on run off in West Africa: A review. Hydrology and Earth System Sciences. 2014;18:2789-2801
10. 10. World Bank. World Development Indicators. Washington: International Bank for Reconstruction and Development; 2005
11. 11. Rhodes ER, Atewamba C. Climate change impact chain factors in ECOWAS. Journal of Agriculture and Environment for International Development. 2019;113(1):35-78
12. 12. FAO. Land Use. FAO; 2018 [Online]. Available:www.fao.org/statistics/en[Accessed: 15-09-2018]
13. 13. FAO. Agricultural Production Data. 2018 [Online]. Available:www.fao.org/statistics/en[Accessed: 15-09-2018]
14. 14. World Bank. World Development Indicators. Washington: International Bank for Reconstruction and Development; 2015
15. 15. Le Q , Nkonya E, Mirzabaev A. Biomass Productivity-Based Mapping of Global Level Degradation Hotspots. Bonn: ZEF, University of Bonn; 2014
16. 16. Kaufman JB, Bhomia R. Ecosystem carbon stocks of mangroves across broad environmental gradients in west-Central Africa: Global and regional comparisons. PLoS One. 2017;12(11)
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26. 26. UNESCO. UNESCO Science Report: Towards 2030. Paris, France: United Nations Educational, Scientific and Cultural Organization; 2015
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28. 28. Zilberman D, Lipper L, McCarthy N, Gordon B. Innovation in response to climate change. In: Climate Smart Agriculture: Building Resilience to Climate Change. Vol. 52. Springer; 2018
29. 29. Torres C, van Seters J. Overview of Trade and Barriers to Trade in West Africa: Insights in Political Economy Dynamics, with Particular Focus on Agricultural and Food Trade. Maastricht: European Center for Development Policy Management; 2016
30. 30. Lokonon BK, Egbendewe AYG, Atewamba C. Spatial Implications of Climate Change on Land Allocation and Agricultural Production in ECOWAS. Vol. 17. Accra, Accra, Ghana: United Nations University Institute for Natural Resources in Africa; 2016
31. 31. Stephan G, Schenker O. International Trade and the Adaptation to Climate Change and Variability. Mannheim, Germany: ZEW - Center for European Economic Research; 2012
32. 32. Roudier P, Sultan B, Quirion P, Berg A. The impact of future climate change on West African crop yields: What does the recent literature say? Global Environmental Change. 2011;21(3):1073-1083
33. 33. Butt T, McCarl B, Kergna A. Policies for reducing agricultural vulnerability to climate change in Mali. Climate Policy. 2006;5:583-598
34. 34. World Bank. The Economics of Adaptation to Climate Change: A Synthesis Report. Washington: International Bank for Reconstruction and Development; 2010
35. 35. Shittu A, Kehinde M, Ogunnaike M, Oyawole F. Effects of land tenure and property rights on farm households’ willingness to accept incentives to invest in measures to combat land degradation in Nigeria. Agricultural and Resource Economics Review. 2018;47(2):357-387
36. 36. Neate P. Water harvesting boosts yield in the Sahel. In: Climate Smart Agriculture Success Stories from Farming Communities Around the World. CGIAR Research Programme on Climate Change, Agriculture and Food Security (CCAFS) and Technical Center for Agriculture for Agricultural and Rural Cooperation (CTA); 2013
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38. 38. Aklesso YGE, Lokonon BOK, Atewemba C, Coulibaly N. Can intra-regional food trade increase food availability in the context of global climatic change in West Africa? Climatic Change. 2017;145(1-2):101

Written By

Calvin Atewamba and Edward R. Rhodes

Submitted: October 15th, 2018 Reviewed: July 8th, 2019 Published: January 8th, 2020


text:
## Fitting 4 parameter distributions in S-Plus (or R)

Hi, I am trying to fit sample data to a Johnson SU distribution in S-Plus. It seems not many people use S-Plus, so if you are familiar with R then you could help as well.

The code that I have is:

f.Jsu.fun.takeslist(x,g,l,r,e)
which is a function I have made that calculates the PDF of each value of the list x and has parameters g,l,r,e corresponding to the Johnson SU distribution. I know this PDF works because I have used it to plot graphs.

fitdistr(turn$all.turn.y.obs,f.Jsu.fun.takeslist,list(g=0.5,r=3,l=3000, e=-200)) is then what I am trying to use to fit the Johnson SU distribution. fitdistr is a native S-Plus function. Now, the fitdistr doesn't work on this function. What I have done previously though is fitted the Gumbel distribution using the same approach by creating my own PDF function, and fitdistr worked and provided a good fit. The Gumbel distribution is 2 parameter and the Johnson SU is 4 parameter, so I am thinking it is just too many parameters for it to handle, although no limits are specified for fitdistr. I am by no means a master of S-Plus or R so I would appreciate anything you guys have to say on this. Thanks!  PhysOrg.com science news on PhysOrg.com >> 'Whodunnit' of Irish potato famine solved>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change>> Curiosity Mars rover drills second rock target  Can you guarantee that turn$all.turn.y.obs follows a Johnson SU? If you can't then maybe the fit is just not good, anyhow it might also be worth to look for outliers in you data. The number of parameters should not be the problem, if anything you could also try to increase the number of max iterations for the optimizers used by fitdistr.

format: plain


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# Canoe riding using your boomerang as motor

These last weeks many of us have been following the olympics.
I was watching the canoe races and was impressed by the skill and energy of athletes.

I thought if an olympian would have several boomerangs and the skills to be able to throw them in a way that he can get them back. If he repeats this throwing in a regular pace say once per second, could he get propulsion out of this chain of action like a rocket engine and make the canoe move? Assuming he is skillful enough to throw them in a way that they burn most of their energy in the air as drag?

Example and some numbers
So he ejects them with high speed and retrieve them with low speed?
lets say an efficient boomerang thrower uses 1 kilogram boomerangs and throw them at a speed of 36 kilometers/hour at a rate of one per second. So he is exerting $E=1/2 (1.(9.8)*(36*1000/3600)^2= 500 watts$ which is beyond our dream but Olympians may be able to do it.
If he can make them come back and land gently on the basket he has for them he can produce o.7 horse power! It would be an exciting game to watch.

• From what I found on the net the speed of the boomerang is about constant, and cannot be tuned . The motion of the boat will be another complication. It is not clear that the boomerang will undershoot so as to be caught further forward than the original throw point. Possibly special design boomerangs might. And then again possibly not. – anna v Aug 23 '16 at 5:19
• Interesting thing is the speed of boomerang really doesn't matter beyond the release point. it's just a media to let the arm of the Olympian work creating the momentum, which will have equal momentum in opposite direction on canoe. For all intensive proposes we could consider the boomerangs as a bucket which he fills with water and throws out fast, albeit the boomerang idea would be nicer for a YouTube video clip. How ever I believe the ballasting the airfoils and designing the pitch and angle and aspect ratio of the boomerang will change its flight and momentum loading or handling properties! – kamran Aug 23 '16 at 6:06


text:
# zbMATH — the first resource for mathematics

Efficient analysis of concurrent constraint logic programs. (English) Zbl 1418.68052
Lingas, Andrzej (ed.) et al., Automata, languages and programming. 20th international colloquium, ICALP 93, Lund, Sweden, July 5–9, 1993. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 700, 633-644 (1993).
Summary: The standard operational semantics of concurrent constraint logic languages is not confluent in the sense that different schedulings of processes may result in different program behaviors. While implementations are free to choose specific scheduling policies, analyses should be correct for all implementations. Moreover, in the presence of parallelism it is usually not possible to determine how processes will actually be scheduled. Efficient program analysis is therefore difficult as all process schedulings must be considered. To overcome this problem we introduce a confluent semantics which closely approximates the standard (non-confluent) semantics. This semantics provides a basis for efficient and accurate program analysis for these languages. To illustrate the usefulness of this approach we sketch analyses based on abstract interpretations of the confluent semantics which determine if a program is suspension and local suspension free.
For the entire collection see [Zbl 0814.00020].

##### MSC:
 68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) 68N17 Logic programming 68N19 Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) 68Q55 Semantics in the theory of computing
Full Text:
##### References:
 [1] S.D. Brookes and A.W. Roscoe. Deadlock Analysis in Networks of Communicating Processes. $$Distributed Computing$$, 4:209-230, 1991. · Zbl 0717.68006 [2] K.M. Chandy and J. Misra. Deadlock Absence Proofs for Networks of Communicating Processes. $$Information Proc. Letters$$, 9(4):185, 1979. · Zbl 0456.68030 [3] M. Codish, M. Falaschi, and K. Marriott. Suspension Analyses for Concurrent Logic Programs. $$ACM Transactions on Programming Languages and Systems$$, 1993. To appear. [4] C. Codognet, P. Codognet, and M. Corsini. Abstract Interpretation for Concurrent Logic Languages. In S. Debray and M. Hermenegildo, editors, $$Proc. North American Conf. on Logic Programming'90$$, pages 215-232. The MIT Press, Cambridge, Mass., 1990. [5] P. Cousot and R. Cousot. Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In $$Proc. Fourth ACM Symp. Principles of Programming Languages$$, pages 238-252, 1977. [6] C.A.R. Hoare. $$Communicating Sequential Processes$$. Prentice-Hall, 1985. · Zbl 0637.68007 [7] J.-L. Lassez and M. J. Maher. Closures and Fairness in the Semantics of Programming Logic. $$Theoretical Computer Science$$, 29:167-184, 1984. · Zbl 0547.68034 [8] J. W. Lloyd. $$Foundations of Logic Programming$$. Springer-Verlag, Berlin, 1987. Second edition. · Zbl 0668.68004 [9] R. Milner. $$Communication and Concurrency$$. Prentice-Hall Int. (UK), 1989. [10] W. Peng and S. Purushothaman. Data flow analysis of communicating finite state machines. $$ACM Transactions on Programming Languages and Systems$$, 13(2):399-442, 1991. [11] V. Saraswat, M. Rinard, and P. Panangaden. Semantic Foundation of Concurrent Constraint Programming. In $$Proc. Eighteenth Annual ACM Symp. on Principles of Programming Languages$$, 1991. [12] V. A. Saraswat. $$Concurrent Constraint Programming Languages$$. PhD thesis, Carnegie-Mellon University, January 1989. Also in $$ACM Distinguished Dissertation Series$$. [13] E. Y. Shapiro. The family of concurrent logic programming languages. $$ACM Computing Surveys$$, 21(3):412-510, 1989. [14] R. Yang and H. Aiso. P-Prolog: a parallel language based on exclusive relation. In E. Y. Shapiro, editor, $$Proc. Third Int'l Conf. on Logic Programming$$, volume 225 of $$LNCS$$, pages 255-269. Springer-Verlag, Berlin, 1986. · Zbl 0595.68010 [15] K. Yelick and J.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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Search: All articles in the CMB digital archive with keyword endomorphisms

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1. CMB 2006 (vol 49 pp. 371)

Floricel, Remus
 Inner $E_0$-Semigroups on Infinite Factors This paper is concerned with the structure of inner $E_0$-semigroups. We show that any inner $E_0$-semigroup acting on an infinite factor $M$ is completely determined by a continuous tensor product system of Hilbert spaces in $M$ and that the product system associated with an inner $E_0$-semigroup is a complete cocycle conjugacy invariant. Keywords:von Neumann algebras, semigroups of endomorphisms, product systems, cocycle conjugacyCategories:46L40, 46L55
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# Tag Info

## Hot answers tagged lilypond

13

Use \once \set chordChanges = ##f at the location where you want to force the chord symbol. \score { << \new ChordNames { \set chordChanges = ##t \chordmode { \repeat volta 2 {g1} \alternative { {c} {\once \set chordChanges = ##f c4 g c c} } } } \new Voice = "one" { \relative c'' { ...

10

I've stumbled up on the answer to my own question. Either of the following should work: \set restNumberThreshold = #1000 % Some large number \override MultiMeasureRestNumber #'stencil = ##f The first is a bit hackish and not very robust (it sets the number of rests required to display the number extremely high), but the second may have unintended ...

8

I'm assuming you are turning a hand- written score into a digital one. You're problem is that you have written this: f8 b4 a8[ g] f2 The key signature shows that F, A, and G need to be sharped, but you've written then as naturals. Try this: fis8 b4 ais8[ gis] fis2 The "-is" tells Lilypond that you want that note sharped, an "-es" tells ...

7

Maybe the command \divisioMinima shown for Gregorian chant notation would be a hack for you. I have not checked, if it can be followed by a bar. Same thing but other notation would be f1 \bar "'" g1 which yields: However, this both are bar lines which could confuse your lilypond interpreter. If you are not checking the bar length, it should not be a ...

7

The usual advice for this is \layout { \context { \Staff \RemoveEmptyStaves }}. Does that do what you want? For breaks at non-bar-line point the usual trick is to insert an invisible bar line via \bar"".

7

LilyPond's input is key-independent. While in equal-tempered tuning the absolute pitch of C sharp and D flat are the same, the musical/scale function is different. Scientific pitch notations usually retain that difference even though basically all keyboards (and the Midi standard) drop it. LilyPond also retains that difference and preserves it even when ...

6

Here are two possible solutions. 1: You don't seem to need two voices from aes8 onwards, so use this: \relative c' { << { c4 c c c8 c c4 bes8 aes4. aes8 aes } \\ { g8 aes f g4 aes f8 aes8 g f r8 r2 } >> << { bes8 bes2 } \\ { f8 g ees f4 } >> aes8( g f <f ees>4.) g8 ees des \clef treble } 2: You can ...

6

Leaving out the number is an approach I have never seen in classical orchestral scores. Typically the last tutti note has a fermata, followed by a one-bar rest also having a fermata above the text "Cadenza". Of course, this leaves open, when to start again, which is the reason, why classical cadenzas end with a trill to be easily recognized. In smaller ...

6

Please read the magnificent documentation at lilypond.org specifically: http://lilypond.org/doc/v2.17/Documentation/usage/command_002dline-usage music.ly: #(use-modules (guile-user)) #(format #t "Using style sheet: ~a\n" style-sheet) \include #style-sheet \relative { c' d e } style-default.ily: % style defs Then run, lilypond -e '(define-public ...

6

In newer versions of LilyPond \override MultiMeasureRestNumber #'stencil = ##f can be expressed as \override MultiMeasureRestNumber.stencil = ##f or even shorter as \omit MultiMeasureRestNumber All of that does exactly the same. It's just syntactic sugar.

6

Use /autochange: \new PianoStaff << \new Staff = "up" { \new Voice = "melOne" { \key g \major \autochange \relative c' { g8 b a c b d c e d8 r fis, g a2 } } } \new Staff = "down" { \key g \major \clef bass } >> For more information, see ...

5

You have to specify the property tupletSpannerDuration to get several tuplets using only one \times command: \set tupletSpannerDuration = #(ly:make-moment 1 8) \times 2/3 {c16 d e d e f } See LilyPond Documentation for more on this.

5

I think that your problem isn't intrinsically with the triplets, but rather with controlling beams; one approach is to manually set the beams: Running lilypond 2.16 on { \times 2/3 {c16^"Two 3-note phrases" d e } \times 2/3 { d e f } r4 r2 \times 2/3 { c16^"Manual Beaming" [d e] d [e f] } r4 r2 \set tupletSpannerDuration = #(ly:make-moment 1 8) \times ...

5

The Bar Numbers and Rehearsal Marks segments of the documentation indicate how to do this: c1 | c1 | c1 | c1 %location where music has been elided % I'd do something like: s1^"2nd Movement Deleted" | s1 | s1 | s1 \break % which inserts a line of blank bars, with a comment above % indicating what has been removed %reset the bar-number counter to the ...

5

Yes, you're right - you must declare the variable before using it. Hope this helps: verseText = "Verse" verseNotes = \relative c' { d8^\markup { \verseText } d d d16 d d8 a r4 | cis8 cis cis cis16 cis cis8 a r4 | } verseSection = \relative c' { \repeat volta 2 { \verseNotes } gis'1 | ...

5

You can both load definitions that change the input name of notes (e.g. the German style definition changes the input syntax for a 'b' to 'h') and apply automatic transpositions (\transpose c e {...}). Between those two features, you should be able to notate anything in any way you want.

5

I'm guessing 'cg' is for conga, given that most of them start like that. I'm pretty sure: o = open tone m = muted tone ss = slap? sidestick So 'cgho' = Conga high open tone; 'cglm' = Conga low muted tone. I'm not sure why the 's' for slap is doubled and lacks a 'cg'. If you aren't familiar with these terms, you should be, since you're writing for it. ...

5

The answer is "Yes you can, but doing this is a really bad idea". It's a bad idea because you will probably soon want to write C natural or F natural with a D major key signature, and if you make "c" mean "c sharp" you won't have a good way to do that. If the key signature changes during the piece, things will quickly get very confusing. Check out "note ...

5

The problem is that this is not a common notation, and the meaning of the symbol "C/Em" is unclear. What Lilypond can do - as you know - is add a letter after a slash, e.g. C/E, which means that you're supposed to play a C major triad with the note E in the bass. What does exist are polychords where two different chords are stacked on top of each other. ...

5

I got an answer from Knute Snortum on the LiliyPond mailing list here After my score block I can add a markup block like this \markup { \column { \line { \null } \line { 2. Here I go } } } It turns out that this is covered in the LilyPond documentation (printing stanzas at the end) but they use the term 'stanza' and so my ...

4

Try something like \version "2.18.2" Amen = << \new Staff << \key g \major \relative c'' { \voiceOne g2 g \bar"|." } \new Voice \relative c' { \voiceTwo e2 d \bar"|." } >> \new Lyrics \lyricmode { A2 -- men. } \new Staff << \key g \major \clef bass \relative c' { \voiceOne c2 b \bar"|." ...

4

It's worth pointing out that as of LilyPond 2.17.11, you can write \tuplet 3/2 8 {c16 d e d e f} and get 3:2 tuplets in groups of duration 8 (in this case, two groups of three tuplets each). This is basically the same as temporarily overriding tupletSpannerDuration.

4

You can, of course, write < g a c e a >4 q q2 If you want to mix different chords, this is not feasible. With the restriction of always needing a duration, you can write something like makevoicing = #(define-scheme-function (parser location m) (ly:music?) (define-music-function (parser location d) (ly:duration?) ...

4

You can extend the two-voice stuff longer but you don't need spacer rests in the second voice. The musical expression is as long as the longest voice. Further the rests in the second voice look unnatural. I would use spacer rests here. \relative c' { << { c4 c c c8 c c4 bes8 aes4. aes8 aes } \\ { g8( aes f g4) aes f8 aes8( g f s8 ...

4

Try song = { \repeat volta 2 { a1 } \alternative { { a } { b } } \bar "|." } harmonies = \chordmode { a1 b c } \score { << \new Staff = "melody" \with { \accepts ChordNames } << \new ChordNames { \set chordChanges = ##t \set noChordSymbol = ##f \override ...

4

\version "2.18.2" \header { title = "Title" composer = "Composer" } \paper { markup-system-spacing #'basic-distance = #50 } \relative c' { c } See here for more information.

4

It isn't Lilypond, but the similarly-text-based ABC notation format has an open source javascript renderer named abcjs, which you might find interesting.

4

The Auto_beam_engraver does not beam over rests, bar lines, manual beams or breathing signs. The Notation Reference is quite explicit regarding the beaming across rests: "Beams must be entered manually if beams are to be extended over rests."

4

While reorganizing your material as shown in the alephzero reply may make independent sense, if you don't want to see instrument names in staves, just adding \context { \Staff \remove "Instrument_name_engraver" } to the inside of your \layout block might get rid of any interpretation of the respective properties. They'll still be set. Note that most ...

4

In order not to complicate the example by adding additional spacing until LilyPond prefers to pick a kneed beam on its own, I am using a voicing change to get this, moving from "first voice" settings in the lower staff to "fourth voice" setting in the higher. Usually \voiceOne/\voiceTwo (can be implied by << ... \\ ... >>) should be used for the ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# Why do tropical cyclones not tear themselves apart?

A tropical cyclone is the generic term for a hurricane, typhoon, or tropical storm. Tropical cyclones derive their energy from evaporation of water at the ocean surface which ultimately recondenses when it cools to the saturation point. The rotation of a tropical cyclone is caused by the Coriolis effect.

What is unclear to me is: Why do these massive bodies of warm, moist air clump together over thousands of kilometers? What physical process causes them to be drawn in towards the center of the storm?

*image taken from the Wikipedia article on tropical cyclones

• The tropical cyclogenesis article on wikipedia describes how cyclones form, but I'm not sure it answers this question. Maybe the answer is just "extreme values of all of the above"? – naught101 Apr 17 '14 at 11:00
• angular momentum, is my suspicion. – Neo Apr 18 '14 at 4:25
• This image shows the evolution of wind pattern in tropical cyclogenesis. The storm eventually becomes large enough for the Coriolis force to balance out the other forces(pressure gradient force), which causes the wind flow to become geostrophic (parallel to isobars) close to the eye of the storm. Tropical systems typically weaken after losing their heat source (ocean), but strong steering flow winds can also shear a hurricane apart by disrupting the aforementioned balance. Illustration of forces – DrewP84 Apr 18 '14 at 4:40
• I should clarify that the winds are not truly geostrophic but instead quasi-geostrophic. – DrewP84 Apr 18 '14 at 4:50
• @DrewP84 Thanks for the response. Do you want to turn it into a full answer? I'll accept and upvote it if you do. – Chris Mueller Apr 18 '14 at 16:10

The equation of motion for a fluid parcel in the atmosphere (in Cartesian space) is

$$\dfrac{D\mathbf u}{Dt} = -\dfrac{1}{\rho}\nabla p-2 \mathbf \Omega \times \mathbf u + \mathbf g + \mathbf F,$$

where $\mathbf u$ is the wind, $\rho$ is density, $p$ is pressure, $\mathbf\Omega$ is the angular velocity of the Earth, $\mathbf g$ is gravity and $\mathbf F$ is friction. The derivative is a material derivative (Lagrangian perspective) where

$$\dfrac{D\varphi}{Dt} = \dfrac{\partial\varphi}{\partial t} + \mathbf u\cdot\nabla\varphi.$$

There is a non-dimensional number called the Rossby number ($Ro$) that determines when a flow behaves geostrophically. This number is given by

$$Ro = {U\over fL},$$

where $U$ is a velocity scale, $L$ is a length scale and $f$ is the Coriolis parameter ($f=2\Omega\sin\phi$, $\Omega = 7.2921 \times 10^{-5}\ \text{s}^{-1}$, and $\phi$ is latitude). When $Ro << 1$, the flow exhibits geostrophic balance. This occurs when $L$ becomes large, which it does as the storm grows. When I say the flow is geostrophic, what I really mean is that the net acceleration of a parcel is small. In a tropical cyclone the isobars are roughly circular and this curvature gives rise to the gradient wind balance.

The gradient wind is the balance of the pressure gradient force, Coriolis force and centripetal acceleration. In this flow, just as in geostrophic flow, the wind will follow the isobars, flowing cyclonically around the center of low pressure, though slower than a geostrphic flow with the same pressure gradient. Close to the ocean surface friction plays a role, and for the near surface winds the friction will cause the wind to be slightly deflected toward low pressure, or inward across the isobars.

Close to the center of the storm, in and near the eyewall, the length scale $L$ is reduced and the Coriolis force places a smaller role. Here the flow attains cyclostrophic balance -- a balance between centrifugal and pressure gradient forces.

The gradient and cyclostrophic balances explain the wind rotating around the storm and surface friction will give a radially inward component at low levels, advecting angular momentum toward the center of the storm. Convection in the eyewall will lift air to the tropopause where it will flow anti-cyclonically (due to the thermal wind) away from the storm before subsiding. The core of the storm is warm and the air there is subsiding, creating the cloud free eye. The flows around the storm are balanced flows and the flow inward/upward/outward/downward is a thermodynamic carnot engine.

This gives us a fairly stable setup and this is why once a tropical storm forms it tends to persist rather than tear itself apart. The key to sustaining this balance is a warm ocean surface and weak vertical windshear. If you take away the warm ocean the storm will start to spin down and if you have strong shear you will disconnect the lower and upper level circulations and the storm will weaken.

• +1 This is the correct answer. – milancurcic May 4 '14 at 5:22


text:
# How do I reduce the space between the caption of the image and normal text?

I am using the osameet3 package and am working with multicol. The image will only import if i use \begin{figure}[H], however this is causing strange extra space between the caption and the rest of my text.

• Please show what you have tried, from \documentclass... to \end{document} --- no more than 2 pages and a figure using lipsum for text filling. Where is the osameet3 package (class?) ? In general it is not a good idea to use the [H] positioning option. – Peter Wilson Apr 13 '20 at 16:59

• px usually refers to the resolution of a screen. It is not one of the dimension units recognized by (La)TeX. pt would be more appropriate, or some multiple of a derivative unit, e,g,, -1.5\baselineskip. (It would go within the figure environment, just before the end.) – barbara beeton May 13 '20 at 19:56


text:
# Multiplying primitive roots of unity.

1. Jul 30, 2013

### Artusartos

1. The problem statement, all variables and given/known data

Let $ζ_3$ and $ζ_5$ denote the 3rd and 5th primitive roots of unity respectively. I was wondering if I could write the product of these in the form $ζ_n^k$ for some n and k.

2. Relevant equations

3. The attempt at a solution

We know that $ζ_3$ is a root of $x^3=1$, and $ζ_5$ is a root of $x^5=1$, so $ζ_3ζ_5$ must be a root of $x^{15}=1$, right?...so $ζ_3ζ_5 = ζ_{15}$. And in general $ζ_nζ_k = ζ_{[n,k]}$, where [n,k] denotes the lcm of n and k. Is that right?

Also is it true that $ζ_{15}^8 = ζ_{15}$? If so, then why/how?

Thank you in advance

2. Jul 30, 2013

### micromass

Staff Emeritus
You got to be careful to specify which root you work with. It is certainly true that $\zeta_{15}^8$ is a primitive 15th root of unity, but it might not be the same one!

For example, in $\mathbb{C}$, we have $\zeta_{15} = e^{2\pi i /15}$ is a possible choice. But then $\zeta_{15}^8 = e^{2\pi i (8/15)}$ is a 15th root of unity but not the same one.

It is indeed true that $\zeta_3\zeta_5$ is a primitive 15th root of unity. And depending on how you defined $\zeta_{15}$, equality holds. For example:

$$e^{2\pi i/3} e^{2\pi i/5} = e^{ 2\pi i (8/15) }$$

So this is a primitive 15th root of unity. But it is not $\zeta_{15}$ if you defined $\zeta_{15} = e^{2\pi i /15}$.

3. Jul 30, 2013

### Boorglar

Perhaps instead of using $ζ_{n}$ to represent a particular primitive n-th root, you might use it to denote the whole set of primitive n-th roots. Then change "=" with $\in$, and define the product of two sets as the set containing all possible products of elements from either set. Then what you say will be true.

Last edited: Jul 30, 2013
4. Jul 30, 2013

### Artusartos

Thanks. We can also conclude that $\Bbb{Q}(\zeta_{15}^8) = \Bbb{Q}(\zeta_{15})$ since both are primitive roots of unity and $\zeta_{15}^{8k}=\zeta_{15}$ and $\zeta_{15}^m = \zeta_{15}^8$ for some $k$ and $m$, right?

5. Jul 30, 2013

### micromass

Staff Emeritus
Sure.

6. Jul 30, 2013

### CompuChip

But note that it doesn't work for $\zeta_{15}^5$, for example.


text:
# RayCast seems to ignore some objects?

I'm currently using a Raycast both for my movement check aswell as a focus-setting check, both checks use pretty much the same code. The problem i'm having is that the Raycast goes through some objects and targets the background no matter what i've tried to far. As you can see in this screenshot, I first clicked on the black sphere (Just a 3D Sphere in my 2D world with a default Sphere Collider) and the Log shows so aswell, however when i click on the white box which the second Debug Log is supposed to be, it just ignores the box collider and goes straight to the Background (the green sprite). The same problem with the Interactable check, code works completely fine with the Sphere but not with the box. Here's the Code i currently use:

    //Movement
if (Input.GetKeyDown(KeyCode.Mouse0))
{
Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
RaycastHit hit;

if (Physics.Raycast(ray, out hit, 100))
{
Debug.Log("We hit " + hit.collider.name + " " + hit.point);
RemoveFocus();
targetPosition = hit.point;
}
}
if(targetPosition != (Vector2)transform.position)
transform.position = Vector3.MoveTowards(transform.position, targetPosition, maxSpeed * Time.deltaTime);

//Check for Interactable, pretty much same code...
if (Input.GetKeyDown(KeyCode.Mouse1))
{
Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
RaycastHit hit;

if (Physics.Raycast(ray, out hit, 200))
{
Interactable interactable = hit.collider.GetComponent<Interactable>();
if(interactable != null)
{
SetFocus(interactable);
}
}
}

• Is your 2D stuff sprites, or UI? Does your 2D stuff use Physics2D? docs.unity3d.com/ScriptReference/Physics2D.Raycast.html – MichaelHouse May 1 '18 at 2:29
• A screenshot to the components of the white box is in the text, here is the sphere which works as i intend it to. – Veineless May 1 '18 at 3:01
• I've tried playing around with different colliders on the white box, using 3d and 2d colliders etc however nothing seemed to fix the issue, not really sure where to look anymore :( – Veineless May 1 '18 at 3:14


text:
# Fancyhdr package latex ma

Creating headers and footers in Latex can be done by using the package “fancyhdr”. This is a short introduction, showing the most important features of the package. If you know “fancyhdr” and are looking for something particular, refer to the fancyhdr-documentation. First of all, you need to tell Latex to use . TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. Join them; it only takes a minute. This article describes how to customize the page layout of your LaTeX documents, i.e how to change page margings and sizes, headers and footers, and the proper placement of ﬁgures 4 Simple use of fancyhdr To use this package in a LATEX2" document, place the ﬁle shohinblog.com in a directory/folder .

## • Fancyhdr package latex ma •

Here's a way: just tell LaTeX that you want to reserve for the page number \ documentclass{book} \usepackage{fancyhdr} \pagestyle{fancy}. This package allows you to customize headers and footers in the LaTeX document. You can find shohinblog.com The fancyhdr package was created by Piet van Oostrum. Useful Links. fancyhdr user's manual. The documentation describes version or later of the fancyhdr package by George Grätzer (University of Manitoba) in Notices Amer. Math. Soc. . The fancyhdr macro package allows you to customize in LATEX your. To customize the footer and header in your document first import the package fancyhdr with. To get better control over the headers, one can use the package fancyhdr written by Piet van Oostrum. It provides.

## see new video Fancyhdr package latex ma

How to Make Fancy Headers and Footers in a Latex Document Part 1/2

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text:
# Venn diagrams, relative so size of its content

Now I am looking if there is any easy way to create venn-diagrams where the circles/ellipses change size relative to its content. I am basically looking for simple compliments either on the form

or with three elements

The output I am looking for is somewhat along these lines

Where the size of the circles are relative to their percentages or probability. (Larger circles, larger probability) and the largest circle represents 1 or 100%

Now is it possible creating a macro that allows one to create such images? Example, given that A=40 , B=60 , A \cap B = 20

-
In principle yes, but the math will be horrible –  Tom Bombadil Jul 9 '12 at 21:32
Horrible? You are speaking to a math undergrad ;) I am sure a solution can be aquired using the \calc package. –  N3buchadnezzar Jul 9 '12 at 21:45
Horrible. Try solving for d in equation (14) in mathworld.wolfram.com/Circle-CircleIntersection.html –  JLDiaz Jul 9 '12 at 22:10
I did, gave me 4 solutions. However latex was not able to interpret the input, I probably did something wrong. –  N3buchadnezzar Jul 9 '12 at 22:11
Recommend that you consider using rectangles instead of circles. Because there are many combination which cannot be displayed with circles. eg Sample space=100 A=60, B=40, A \cap B =20; cannot be done with circles. Additionally the computations with rectangles will be trivial. –  R. Schumacher Jul 10 '12 at 3:07

The answer is "impossible". You can't draw circles with the requested values : A=.40 , B=.60 , A \cap B = .20 like R. Schumacher wrote.

\documentclass[11pt]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{fourier}
\usepackage{tikz,verbatim}
\usetikzlibrary{arrows,patterns}

\begin{document}

\begin{tikzpicture}[scale=4,>=latex']
\node[above right,magenta] at (0,1) {$\mathcal{C}$};
\draw (0.63245-1,0) circle [radius=0.63245cm];   % sqrt(0.4)
\draw (1-0.77459,0) circle [radius=0.77459cm];   % sqrt(0.6)
\node[above right] at (-1,0) {$\mathcal{C}_a$};
\node[above left] at ( 1,0) {$\mathcal{C}_b$};
\draw[->] (-1,0)--(1.2,0);
\draw[->] (0,-1)--(0,1.2);
\filldraw[blue] (0.63245-1,0) circle(.4pt) -- node[above right]{$ra\approx 0.632$}++(60:0.63245);
\filldraw[blue] (1-0.77459,0) circle(.4pt) -- node[above right]{$rb\approx 0.774$}++(60:0.77459);
\draw[magenta,<->] (0,0) -- node[below]{1} (1,0);
\clip (0.63245-1,0) circle [radius=0.63245cm];   % sqrt(0.4)
\clip (1-0.77459,0) circle [radius=0.77459cm];   % sqrt(0.6)
\draw[red,<->] (0.63245-1,-0.05) -- node[below]{0.59296} (1-0.77459,-0.05);

\node at (-0.25,-0.4){$\mathcal{A}$};
\end{tikzpicture}

\begin{verbatim}
Macro to determine the area of the asymmetric lens.
\pgfmathsetmacro{\ra}{sqrt(0.4)}
\pgfmathsetmacro{\rb}{sqrt(0.6)}
\pgfmathsetmacro{\d}{2-0.63245-0.77459}
\pgfmathsetmacro{\area}{%
(  \ra*\ra*acos((\d*\d-\rb*\rb+\ra*\ra)/(2*\d*\ra))/180*3.1415
+\rb*\rb*acos((\d*\d+\rb*\rb-\ra*\ra)/(2*\d*\rb))/180*3.1415
-0.5*sqrt((-\d+\ra+\rb)*(\d+\ra-\rb)*(\d-\ra+\rb)*(\d+\ra+\rb))
)/3.1415}
\end{verbatim}

\pgfmathsetmacro{\d}{2-0.63245-0.77459}
\pgfmathsetmacro{\ra}{sqrt(0.4)}
\pgfmathsetmacro{\rb}{sqrt(0.6)}
\pgfmathsetmacro{\area}{%
(  \ra*\ra*acos((\d*\d-\rb*\rb+\ra*\ra)/(2*\d*\ra))/180*3.1415
+\rb*\rb*acos((\d*\d+\rb*\rb-\ra*\ra)/(2*\d*\rb))/180*3.1415
-0.5*sqrt((-\d+\ra+\rb)*(\d+\ra-\rb)*(\d-\ra+\rb)*(\d+\ra+\rb))
)/3.1415}

The area of the circle $\mathcal{C}$  is $1\times \pi$.

The area of the circle $\mathcal{C}_a$  is $0.4\times \pi$.

The area of the circle $\mathcal{C}_b$  is $0.6\times \pi$.

If $d=0.59296$  then $\mathcal{A}=\area\times \pi$.

\pgfmathsetmacro{\d}{0.681}
\pgfmathsetmacro{\area}{%
(  \ra*\ra*acos((\d*\d-\rb*\rb+\ra*\ra)/(2*\d*\ra))/180*3.1415
+\rb*\rb*acos((\d*\d+\rb*\rb-\ra*\ra)/(2*\d*\rb))/180*3.1415
-0.5*sqrt((-\d+\ra+\rb)*(\d+\ra-\rb)*(\d-\ra+\rb)*(\d+\ra+\rb))
)/3.1415}

If $d=0.681$  then $\mathcal{A}=\area\times \pi$ but  $0.59296$  is the maximum value of $d$, so it's impossible to draw circles with the requested values.

\end{document}

For others values it's possible to use an iterative approach via nesting intervals (dichotomy) . I find 0.681 with a manual approach but I think it's not very difficult to build an algorithm to find this value.

-