Verifying optimality of rainfed agriculture using a stochastic model for drought occurrence

It may be paradoxical but subsistence rainfed agriculture is the predominant source of food in Sub-Saharan Africa where the production uncertainty is associated with the stochastic nature of rainfall. This paper attempts to comprehend the rationale of this situation by a mathematical approach. Considering the level of drought severity as the zero-reverting Ornstein–Uhlenbeck process, optimality of rainfed agriculture is investigated in the context of stochastic control theory. Occurrence of drought terminating growth of crops is modelled with the concept of first exit time. A stochastic control problem allowing for virtual cost of irrigation, water stress to crops, and benefits of farming is formulated with irrigation effort as the control variable. The Hamilton–Jacobi–Bellman equation governing the optimal control is studied to identify the set of cost functions optimizing rainfed agriculture in an inverse problem approach. Data and information were collected in the coastal savanna agro-ecological zone of Ghana, to identify model parameters, formulate the stochastic control problem, solve the inverse problem, and then verify optimality of rainfed agriculture. The results indicated that rainfed agriculture is not optimal when the crop is more tolerant to water stress.     

Chlorophyll distribution and photosynthetic activity in the north and equatorial Pacific Ocean along 155°W

The distribution of chlorophylla and photosynthetic characterestics of phytoplankters were investigated along 155°W between 50°N and 15°S during the KH-69-4 cruise of the R. V. Hakuh Maru (Aug. 12–Nov. 13, 1969). High concentrations of chlorophylla (more than 0.2 mg Chla/m³) were observed above the depths of 150 m at all stations except in 17°N, 5°S and 15°S. North of 20°N, the depths of chlorophyll accumulation shifted from near the surface to 50–100 m with southwards. In the equatorial region, chlorophyll accumulation centered at a depth of about 70 m and ranged vertically between 10 and 150 m. In all cases in the present study area, chlorophyll accumulation occurred within the euphotic zone (above the depth corresponding to 1% of the surface illumination), and except in the subarctic and some equatorial waters, this was usually prevalent in the lower half of the euphotic zone.The photosynthetic activities (initial slope of P vs I curve) of samples from the depths of chlorophyll accumulation were similar to, or lower than, those of shallow samples from the depths of upper half of the euphotic zone. At the depths of chlorophyll accumulation, calculatedin situ photosynthesis was high in the central Pacific and equatorial waters but low in the subarctic waters.     

Aircraft Observations of Air-mass Modification Over the Sea of Okhotsk during Sea-ice Growth

In order to quantitatively investigate the role of leads and sea-ice in air-mass modification, aircraft observations were conducted over the partially ice-covered Sea of Okhotsk. We investigated two cold-air outbreak events with different sea-ice concentrations. In both cases, the difference between the temperatures of surface air and the sea surface (ΔT) dropped rapidly with the accumulated fetch-width of leads up to about 35-40 km, and then decreased very slowly. The surface sensible heat flux originating from open water was about 300 W m⁻² within a few kilometres from the coast and decreased with increasing accumulated fetch-width. The sensible heat flux was about 100 W m⁻² on average. These results indicate that the downwind air-mass modification depends mainly on the total (accumulated) extent of open water. The total buoyancy flux calculated by the joint frequency distribution method correlated very well with ice concentration. Such a relationship was not clear in the case of the moisture flux . The ratio between rising thermals and cold downdrafts differed significantly between upwind and downwind regions; that is, the buoyancy flux was dominated by in the developing stage of the boundary layer, while also became important after the development of the boundary layer.     

Kinetic stability of a melted iron globule during chondrule formation. I. Non‐rotating model

Abstract— We have investigated the kinematics of the separation of iron globules from chondrules during chondrule formation. A simple model, which assumes that the system has no angular momentum, was used to calculate the energy of a system with an iron globule and a chondrule. The energies of three different states were calculated: 1) a melted iron globule fully embedded in a melted chondrule, 2) a melted iron globule on the surface of a melted chondrule, and 3) a melted iron globule being separated from a melted chondrule. We also calculated the lowest energy shape for a melted iron globule on the surface of a melted chondrule, and compared our result with the shapes of four natural samples of chondrules and iron globules in thin sections. The shapes were calculated using an assumed value for the interface energy between the four couples of melted chondrules and the iron globules, and agree well with the natural shapes of chondrules and iron globules. The results of our calculations show that the iron globules of these four samples would be strongly bound to the surface of the melted chondrule during chondrule formation, and separation would be difficult, if the iron globules had been on the surface of precursors of these chondrules. Our results also show that if these iron globules were initially inside and transported to the surface of the melted chondrule, most of them would be ejected from the inside to outside because of surface tension forces, as long as the energy losses due to viscous dissipation when the globules pass through the surface of melted chondrules were sufficiently small. Although further improvement of the model is required, our results demonstrate that this ejection process may be responsible for the depletion of siderophile elements in natural chondrules.     

Characterization of the amorphous state in metamict silicates and niobates by EXAFS and XANES analyses

X-ray absorption spectroscopy using synchrotron radiation has been applied to the investigation of the coordination geometries around Y, Zr and Nb atoms in metamict zircon, gadolinite, fergusonite, euxenite and samarskite. EXAFS and XANES spectra of their crystalline counterparts and synthetic compounds including ZrO₂, Y₂O₃, YNbTiO₆, YNbO₄, LiNbO₃, and NiNb₂O₆ were also measured for comparison. Metamict zircon shows a significant decrease in its Zr-O bond distances accompanying an increase in distortion of the Zr-O coordination polyhedra as compared with crystalline zircon. On the contrary, the average Nb-O bond distances and the symmetry of the coordination polyhedra around the Nb atoms in metamict euxenite and samarskite resemble those in the crystalline euxenite. Compared with crystalline fergusonite, a decrease in the distortion of the Nb-O octahedra is observed in metamict fergusonite. The structures of the second nearest neighbors (the metal-metal interactions) are largely disrupted in the metamict specimens except for metamict zircon and samarskite with high trivalent iron concentration. Nb in metamict samarskite is in octahedral coordination by oxygen and is similar to that in euxenite.     

Taylor-Görtler vortices expected in the air flow on sea surface waves—I

Taylor-Grörtler vortices are longitudinal vortices resulting from a centrifugal instability. They are generated in the flow having a curved streamline with an increasing velocity in the direction of decreasing curvature.It is shown that the air flow above wind waves and swells also satisfies locally the condition of the centrifugal instability. Numerical calculations indicate the possibility of generation of Taylor-Görtler vortices on the trough of sea waves. For example, when a wind of about 12.2 m/s at 10-m level is blowing over sea waves of the wave length of 15 m like the swell, the critical water wave height beyond which the vortices may be generated is about 0.5 m, and the critical wave length and the height of center of the generated vortices are about 24 m and 3.7 m, respectively. Further, about the relations between the generation of vortices and wind waves, it is shown that the condition of their generation is satisfied at the trough of waves for early stages of the wave generation.In conclusion, it is expected that the Taylor-Görtler vortices change the wind profile along the sea surface, and also, play some part in the growth of wind waves, especially in the formation of their three dimensional structure.     

Assessing the impacts of climate change on rice yields in the main rice areas of China

This paper assesses the impact of climate change on irrigated rice yield using B2 climate change scenario from the Regional Climate Model (RCM) and CERES-rice model during 2071--2090. Eight typical rice stations ranging in latitude, longitude, and elevation that are located in the main rice ecological zones of China are selected for impact assessment. First, Crop Estimation through Resource and Environment Synthesis (CERES)-rice model is validated using farm experiment data in selected stations. The simulated results represent satisfactorily the trend of flowering duration and yields. The deviation of simulation within ± 10% of observed flowering duration and ± 15% of observed yield. Second, the errors of the outputs of RCM due to the difference of topography between station point and grid point is corrected. The corrected output of the RCM used for simulating rice flowering duration and yield is more reliable than the not corrected. Without CO₂ direct effect on crop, the results from the assessment explore that B2 climate change scenario would have a negative impact on rice yield at most rice stations and have little impacts at Fuzhou and Kunming. To find the change of inter-annual rice yield, a preliminary assessment is made based on comparative cumulative probability at low and high yield and the coefficient variable of yield between the B2 scenario and baseline. Without the CO₂ direct effect on rice yield, the result indicates that frequency for low yield would increase and it reverses for high yield, and the variance for rice yield would increase. It is concluded that high frequency at low yield and high variances of rice yield could pose a threat to rice yield at most selected stations in the main rice areas of China. With the CO₂ direct effect on rice yield, rice yield increase in all selected stations.     

A scaling model for quantification of earthquakes in and near Japan

A simple method is developed to determine seismic moments of earthquakes. The method is qualified through criteria such as simplicity of calculations, coverage of wide magnitude range, and insensitivity to detailed instrumental response. The method is applied to 163 major earthquakes which occurred underneath Japan and the Japan Sea in the time from 1926 to 1977. Magnitudes of these earthquakes, which have been determined by the Japan Meteorological Agency, (M_JMA) cover the range from 4.3 to 7.5. At first, source spectra are analyzed through a very simple way introducing two new parameters: characteristic period T_c and seismic-moment factor M_c. The former is defined as an average value of apparent periods of seismic waves with the maximum trace amplitude at many stations. The latter is an average of products of maximum trace amplitude and its apparent period multiplied by epicentral distance. It is shown that T_c corresponds to the period of the corner frequency of an earthquake and M_c to the seismic-moment density at the period of T_c. A scaling model of earthquake source spectra is presented which satisfies the empirical relations between the surface-wave magnitude M_s and M_JMA, and M_JMA and the body-wave magnitude m_b. Those relations are independent of the Gutenberg and Richter relation between M_s and m_b, because M_JMA is determined from maximum amplitudes of seismic waves with a period of about 4 sec. The static seismic moment of each earthquake can be estimated from calculated M_c using the source spectra of the scaling model. Seismic moments of 18 earthquakes determined by conventional analyses from near- and/or far-field observations are consistent with static seismic moments thus estimated over the range from 2 × 10²³ to 3 × 10²⁷ dyne cm. This shows the potential in practice of the present method, especially in the routine processing of seismic data.     

Further characterization of carbonaceous materials in Hayabusa‐returned samples to understand their origin

Carbonaceous materials in the sample catcher of the Hayabusa spacecraft were assigned as category 3 particles. We investigated the category 3 particles with a suite of in situ microanalytical methods. Possible contaminants collected from the cleanrooms of the spacecraft assembly and extraterrestrial sample curation center (ESCuC) were also analyzed in the same manner as category 3 particles for comparison. Our data were integrated with those of the preliminary examination team for category 3 particles. Possible origins for the category 3 particles include contamination before and after the operation of the Hayabusa spacecraft.