Regional gravity field model in Pakistan area from the combination of CHAMP,GRACE and ground data using least squares collocation: A case study

This study describes a methodology of recovery of the Earth’s gravity field from CHAMP and GRACE satellites data in Pakistan using least squares collocation (LSC) based downward continuation technique. The CHAMP height anomalies and GRACE gravity disturbances derived from the observed satellite data have been used in combination solution using LSC with observed gravity values at the Earth surface. The combined covariance functions of height anomalies and/or gravity disturbances at satellite altitudes and observed gravity anomalies at Earth surface have been used as the basis for combination and downward continuation solution. The variance of predicted gravity anomalies from GRACE gravity disturbances is relatively lower than the corresponding results of gravity anomalies from CHAMP height anomalies. This fact may be attributed partly to the amplification of noise and partly to the unstable inverse transformation process of height anomalies to gravity anomalies. The impact of data error variance has been studied in the context of smoothing and noise reduction in the final solution of downward continuation using least squares collocation. The raising of data error suppresses the noise and as a result a smooth final solution is obtained. The prediction results appear to be dependent on the quality of data and goodness of combined covariance function, which are fairly comparable for the CHAMP and GRACE data. The recovered gravity field from satellite data appears to contribute mainly to medium and long wavelength parts of total gravity field spectrum. Due to flexibility of data handling in least squares collocation, this procedure is applicable to any observable of gravity field being at different altitudes and with different data spacing.     

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.     

On the selection of optimal global geopotential model for geoid modeling: A case study in Pakistan

A statistical comparison has been made between gravity field parameters derived from different global geopotential models (GGMs) and observed gravity anomalies, gravimetric geoid and GPS-Leveling data. The motivation behind this study is the selection of best possible global geopotential model that best matches statistically with the local observed data in Pakistan. This will facilitate in decreasing the load on observed data for the development of regional gravimetric geoid in remove-compute-restore technique when used in the Stokes’s integral for computation of the residual part. It is observed that combined geopotential models such as EGM96 and PGM200A, EIGEN-GL04C and EIGEN-CG03C reflect the better match in the total spectral range of gravity and GPS-Leveling data. Results of the precise local geoid model also indicate similar characteristics. A very-high-degree model “EGM2008” (degree/order 2160) exhibits relatively superior statistical fit with observed ground data in Pakistan region. For satellite-only models an increasing trend in the standard deviation can be seen with maximum of about ∼4 m in difference between GPS-Leveling and corresponding GGM’s geoid with increase in the order from 50 to 120 and then it decreases afterwards. However, for the EIGEN-CHAMP03SP, standard deviation saturates to a value of 3.4 m. This is an indication of contamination in the long to medium wavelength part, i.e. 50–100° for the satellite-only models. Moreover, the models DEOS-CHAMP-01C, GGM02C and then ITG-GRACE03 appear to have better fit for medium to long wavelength and can possibly be recommended for use as long wavelength part with the local observed data. While a hybrid geopotential model selection can be achieved through the selection from either of DEOS-CHAMP-01C, GGM02C, GGM02S, EIGEN-GRACE02S or ITG-GRACE03 in the long wavelength (to degree and order 40) and EGM96, PGM200A, EIGEN-GL04C, EIGEN-CG03C or even EGM2008 in medium to short wavelength, i.e. from degree 41 to maximum degree and order.     

Implications of day temperature variation for an aero-engine's HP turbine-blade's creep life-consumption

Some in-service deterioration in any mechanical device, such as an aero-engine, is inevitable. Also in a country like Pakistan, there is a significant variation of day temperature over the year. As a result of experiencing deterioration (of the engine as a whole or any of its components individually) and/or any alteration in the conditions (such as day temperature) of incoming air stream, an engine will seek a different steady operating point thereby resulting in a variation of the spool speeds and/or turbine-entry temperatures in order to provide the same thrust. Rises in the turbine entry-temperatures and spool speeds result in greater rates of creep and fatigue damage being incurred by the hot-end components and thereby higher engine's life cycle costs.Possessing a better knowledge of the impacts of day temperature variation upon the creep life-consumption of aero-engine's hot-end components, helps the users to take wiser management-decisions. For a military aircraft's mission-profile, using a bespoke computer simulation, the implications of day temperature variation for a turbofan aero-engine's high pressure turbine-blade's creep life-consumption have been predicted.