Evaluation of three high-resolution satellite precipitation estimates: Potential for monsoon monitoring over Pakistan

Multi-sensor precipitation datasets including two products from the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) and estimates from Climate Prediction Center Morphing Technique (CMORPH) product were quantitatively evaluated to study the monsoon variability over Pakistan. Several statistical and graphical techniques are applied to illustrate the nonconformity of the three satellite products from the gauge observations. During the monsoon season (JAS), the three satellite precipitation products captures the intense precipitation well, all showing high correlation for high rain rates (>30 mm/day). The spatial and temporal satellite rainfall error variability shows a significant geo-topography dependent distribution, as all the three products overestimate over mountain ranges in the north and coastal region in the south parts of Indus basin. The TMPA-RT product tends to overestimate light rain rates (approximately 100%) and the bias is low for high rain rates (about ±20%). In general, daily comparisons from 2005 to 2010 show the best agreement between the TMPA-V7 research product and gauge observations with correlation coefficient values ranging from moderate (0.4) to high (0.8) over the spatial domain of Pakistan. The seasonal variation of rainfall frequency has large biases (100–140%) over high latitudes (36N) with complex terrain for daily, monsoon, and pre-monsoon comparisons. Relatively low uncertainties and errors (Bias ±25% and MAE 1–10 mm) were associated with the TMPA-RT product during the monsoon-dominated region (32–35N), thus demonstrating their potential use for developing an operational hydrological application of the satellite-based near real-time products in Pakistan for flood monitoring.     

Collinear equilibrium points in the elliptic R3BP with oblateness and radiation

We have studied the positions and stability of the collinear equilibrium points, L_1,2,3 of an infinitesimal body in the elliptic restricted three-body problem (ER3BP) when both primaries of the system are luminous and oblate spheroids moving in elliptic orbits around their common center of mass. We observe that their positions are affected by the radiation pressure forces, oblateness and the eccentricity of the orbits, but the stability character remains unchanged and are unstable. The effects of the parameters involved on the collinear points, in particular for the binary systems Achird, Luyten 726-8, Kruger 60, Alpha Centauri AB and Xi Bootis, and their stability in general have been investigated numerically using the analytical results obtained.