Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the \(4 \pi \) fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as \(2^{30}\,{\approx }\,10^9\). The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.     

A method solving kepler's equation without transcendental function evaluations

We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series expansion. A combination of these was applied to solving Kepler's equation for the elliptic case. The resulting method requires no evaluation of transcendental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original Newton-Raphson method. Also it is more than 2.5 times as fast as Halley's method, Nijenhuis's method, and others.     

Shock metamorphism on the moon

Shock metamorphism of the lunar samples is discussed. All types of lunar glasses formed by various-size collision-type impact are found as impact glass, ropy glass and agglutinates. The agglutinates bonded by crystal and glassy materials contain hydrogen and helium from the solar wind components. Lunar shocked minerals of plagioclase and silica show anomalous compositions and densities. There are typical two formation processes on planetary materials formed by shock events; that is (1) shocked quartz formed by silica-rich target rocks (esp. on evolved planets of the Earth and Mars), and (2) shocked silica with minor Al contents formed from plagioclase-rich primordial crusts of the Moon. The both shocked silica grows to coarse-grain normal crystals after high-temperature metamorphism which cannot distinguish the original main formation event of impact process.     

IOD and ENSO impacts on the extreme stream-flows of Citarum river in Indonesia

Extreme stream-flow events of Citarum River are derived from the daily stream-flows at the Nanjung gauge station. Those events are identified based on their persistently extreme flows for 6 or more days during boreal fall when the seasonal mean stream-flow starts peaking-up from the lowest seasonal flows of June–August. Most of the extreme events of high-streamflows were related to La Ni?a conditions of tropical Pacific. A few of them were also associated with the negative phases of IOD and the newly identified El Ni?o Modoki. Unlike the cases of extreme high streamflows, extreme low streamflow events are seen to be associated with the positive IODs. Nevertheless, it was also found that the low-stream-flow events related to positive IOD events were also associated with El Ni?o events except for one independent event of 1977. Because the occurrence season coincides the peak season of IOD, not only the picked extreme events are seen to fall under the IOD seasons but also there exists a statistically significant correlation of 0.51 between the seasonal IOD index and the seasonal streamflows. There also exists a significant lag correlation when IOD of June–August season leads the streamflows of September–November. A significant but lower correlation coefficient (0.39) is also found between the seasonal streamflow and El Ni?o for September–November season only.     

Probabilistic prediction of Indian summer monsoon rainfall using global climate models

Probabilistic seasonal predictions of rainfall that incorporate proper uncertainties are essential for climate risk management. In this study, three different multi-model ensemble (MME) approaches are used to generate probabilistic seasonal hindcasts of the Indian summer monsoon rainfall based on a set of eight global climate models for the 1982–2009 period. The three MME approaches differ in their calculation of spread of the forecast distribution, treated as a Gaussian, while all three use the simple multi-model subdivision average to define the mean of the forecast distribution. The first two approaches use the within-ensemble spread and error residuals of ensemble mean hindcasts, respectively, to compute the variance of the forecast distribution. The third approach makes use of the correlation between the ensemble mean hindcasts and the observations to define the spread using a signal-to-noise ratio. Hindcasts are verified against high-resolution gridded rainfall data from India Meteorological Department in terms of meteorological subdivision spatial averages. The use of correlation for calculating the spread provides better skill than the other two methods in terms of rank probability skill score. In order to further improve the skill, an additional method has been used to generate multi-model probabilistic predictions based on simple averaging of tercile category probabilities from individual models. It is also noted that when such a method is used, skill of probabilistic forecasts is improved as compared with using the multi-model ensemble mean to define the mean of the forecast distribution and then probabilities are estimated. However, skill of the probabilistic predictions of the Indian monsoon rainfall is too low.     

The role of the intra-daily SST variability in the Indian monsoon variability and monsoon-ENSO–IOD relationships in a global coupled model

The impact of diurnal SST coupling and vertical oceanic resolution on the simulation of the Indian Summer Monsoon (ISM) and its relationships with El Ni?o-Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) events are studied through the analysis of four integrations of a high resolution Coupled General Circulation Model (CGCM), but with different configurations. The only differences between the four integrations are the frequency of coupling between the ocean and atmosphere for the Sea Surface Temperature (SST) parameter (2 vs. 24?h coupling) and/or the vertical oceanic resolution (31 vs. 301 levels) in the CGCM. Although the summer mean tropical climate is reasonably well captured with all the configurations of the CGCM and is not significantly modified by changing the frequency of SST coupling from once to twelve per day, the ISM–ENSO teleconnections are rather poorly simulated in the two simulations in which SST is exchanged only once per day, independently of the vertical oceanic resolution used in the CGCM. Surprisingly, when 2?h SST coupling is implemented in the CGCM, the ISM–ENSO teleconnection is better simulated, particularly, the complex lead-lag relationships between the two phenomena, in which a weak ISM occurs during the developing phase of an El Ni?o event in the Pacific, are closely resembling the observed ones. Evidence is presented to show that these improvements are related to changes in the characteristics of the model’s El Ni?o which has a more realistic evolution in its developing and decaying phases, a stronger amplitude and a shift to lower frequencies when a 2-hourly SST coupling strategy is implemented without any significant changes in the basic state of the CGCM. As a consequence of these improvements in ENSO variability, the lead relationships between Indo-Pacific SSTs and ISM rainfall resemble the observed patterns more closely, the ISM–ENSO teleconnection is strengthened during boreal summer and ISM rainfall power spectrum is in better agreement with observations. On the other hand, the ISM–IOD teleconnection is sensitive to both SST coupling frequency and the vertical oceanic resolution, but increasing the vertical oceanic resolution is degrading the ISM–IOD teleconnection in the CGCM. These results highlight the need of a proper assessment of both temporal scale interactions and coupling strategies in order to improve current CGCMs. These results, which must be confirmed with other CGCMs, have also important implications for dynamical seasonal prediction systems or climate change projections of the monsoon.     

Soil CO2 efflux, carbon dynamics, and change in thermal conditions from contrasting clear-cut sites during natural restoration and uncut larch forests in northeastern China

With the implementation of the Chinese Natural Forest Conservation Program (NFCP) in 1998, over millions of hectares of forest in northeastern China have been protected through natural restoration (closure of hills). The impact of this program on the carbon budget of soil has not been evaluated until now. This paper presents results from a 6-year study of total CO₂ efflux from both soil and litter (R _total), CO₂ flux from soil (R _soil), soil organic matter (SOM), soil microbe density, and litter input and root biomass at an uncut larch (Larix gmelinii) forest and at a natural restoration site. The natural restoration area is a clear-cut site that was formerly part of a continuous portion of the uncut larch forest. Our objectives were to: (1) quantify the magnitude of CO₂ efflux from typical sites in northeastern China; (2) explore the changes in thermal conditions, SOM, and annual CO₂ flux during the 6-year natural restoration, and (3) evaluate the impact of NFCP on soil carbon processes. The annual R _soil at the clear-cut site (58.6–68.2 mol m^???2 year^???1) was 113.6–228.4% (mean 141.5%) higher than that at the uncut larch site (29.6–58.4 mol m^???2 year^???1). At the same time, annual CO₂ from litter at the clear-cut site (2.0–14.2 mol m^???2 year^???1) was only 23.5–84.5% (mean 52.5%) of that at the uncut larch site (5.4–16.8 mol m^???2 year^???1). SOM at the surface layer of the clear-cut site was 75% of that at the uncut larch site, but the soil microbial biomass (carbon) at the clear-cut site was much higher than that at the larch site (p?<?0.05). The percentage of bacteria, fungi and actinomycetes also were largely different between both sites. Natural restoration at the clear-cut site strongly affected thermal conditions. Although the soil temperature (T _soil) and effective accumulated $T_{\rm soil} > 0^{\circ}$ C at the clear-cut site was much higher, the temperature sensitivity (Q ₁₀) was much lower than that at the uncut larch site, and their differences decreased linearly from 2001 to 2006 (p?<?0.05). Moreover, Q ₁₀ at the clear-cut site significantly increased with the progress of natural restoration, which diminished the Q ₁₀ difference between the two sites (slope?=???0.2792, r ²?=?0.4744, p?<?0.05). These data imply that the NFCP natural restoration process has positively recovered the thermal condition of the clear-cut site to the level of uncut larch forest during the 6-year period. However, linear regression analysis showed that the 6-year natural restoration only slightly affected the annual soil CO₂ efflux and SOM at both sites, and also did not diminish the differences between the two sites (p?>?0.10), indicating that a much longer time is necessary to restore the soil carbon in the clear-cut site.     

Long-term precipitation and stream discharge records at seven forested experimental watersheds along a latitudinal transect in Japan: Jozankei,Kamabuchi, Takaragawa,Tsukuba, Tatsunokuchi-yama,Kahoku and Sarukawa

This data note introduces a database of long-term daily total precipitation and stream discharge data for seven forested watersheds in Japan that have been continuously monitored by the Forestry and Forest Products Research Institute. Three of the watersheds started data collection in the 1930s. Forest cover across the sites ranges from cool to warm temperate regions with the latitude spanning from 31 to 44° N and annual precipitation ranging from 1200 to 3000 mm yr⁻¹. The effects of vegetation change via clearcutting, thinning and forest fire (among other stressors) on stream discharge can be analysed from the long-term observation sites. Moreover, this multi-site dataset allows for inter- and intra-site comparisons of annual water loss (difference of annual precipitation and stream discharge). These long-term datasets can provide comprehensive insights into the effects of climate change and other stressors on forested ecosystems, not only in Japan but across a spectrum of forest types, if combined with other long-term records from other forested watersheds across the world.