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Distributed Pixel Method to Speed-Up the RS data assimilation of SWAP Model  ,  ,  Shamim Akhter1, Kiyoshi Honda1, Yann Chemin1 1School of Advanced Technologies, Asian Institute of Technology, Thailand. E-mail: shamim7862002@yahoo.com, Honda@ait.ac.th, yann.chemin@ait.ac.th  Putchong Uthayopas2 2Department of Computer Engineering, Kasetsart University, Thailand Email: pu@ku.ac.th ABSTRACT Agricultural monitoring is necessary for efficient food security management at country level. The near real time monitoring or prediction on crop growth in terms of planting date, acreage, planting intensity, water stress, biomass, yield and etc. is important. It can contribute to better policymaking, timely countermeasures, optimization of water resources distributions, damage assessment and finally to food supply security and stable market. To run crop models are quite useful especially for prediction, however, the parameter determination in large area is in practical a difficult task. We are proposing a methodology to estimate these parameters from remote sensing data. The methodology uses data assimilation technique (optimization is based on Genetic Algorithm), and it can estimate them even though they cannot be seen directly from the remote sensing data. However, this method required extremely high computational power as well as time, thus the application to real situation has been difficult. Cluster is a type of parallel and distributed processing system, provides us with increased computing capabilities. Under the assumption that Cluster style computing will remove computational time constraints, a parallel crop model (SWAP-GA) procedure for remotely sensed images are considered. A numerical experiment with parallel SWAP-GA with distributing pixel is presented in this paper to show the strengths and limitations of the proposed approach using Cluster computers (optima & magi cluster). Introduction Running a crop growth model is useful for agriculture monitoring, prediction and management. A simulation model SWAP has been utilized for theses purposes. SWAP (Soil, Water, Atmosphere, and Plant) is equipped with crop models and water management modules where the growth and development of a crop can be simulated under different climatic and environmental conditions (Van Dam et al. 1997). One problem to run SWAP model is parameter identification, especially when the target area is large such as provincial or country level. Remote Sensing (RS) provides us with useful information over large area. RS cannot observe input parameters of SWAP directly, however, a method to estimate input parameters of SWAP from RS using data assimilation has been proposed (Ines, 2002). This method optimize input parameters to minimize the difference of 2 ETa, those are from remote sensing and SWAP model. GA is being used in this optimization process. The combine process of SWAP model and GA is called SWAP-GA model. Even though the problem with larger RS data is solved, a practical issue arises with the overall calculations time load for assimilating data with remote sensing data. Cluster is the most commonly used parallel computing, which provides us with increased computing capabilities. Under the assumption that Cluster style computing will remove computational time for SWAP-GA, three (3) approaches are proposed by Akhter S.(2005a). 1) All populations will be distributed properly among available slaves by the Master computer. Slaves do the evaluation, generate the fitness and send back the population (with fitness) to the Master. 2) All pixels will be distributed among the available slaves. Each slave will evaluate a total sequential SWAP-GA procedure inside itself for one pixel at a time and will produce a total assimilation result for that pixel in a file in their local Hard Disk. 3) The combined model of distributed pixel and distributed population is called Hybrid model. The results and experiments with distributing pixel method are going to present in this paper. The AIT cluster computers (http://optima.ait.ac.th) and Kasetsart University cluster computers (www.magi.cpe.ku.ac.th) are used for the purpose of experiment. Swap Model SWAP (Soil-Water-Atmosphere-Plant) is the successor of the agro-hydrological model Swatr (Feddes et al., 1978). SWAP integrates water flow, solute transport and crop growth according to current modeling concepts and simulation techniques. SWAP uses daily meteorological data to calculate ETpot according to the Penman-Monteith equation. The ETpot is used to calculate the potential soil evaporation rate (Epot) and potential transpiration rate (Tpot) according to the leaf area index development. Epot is reduced to actual soil evaporation rate (Eact) by taking the minimum of the evaporation rate, the maximum soil water flux in the top soil according to Darcy's law assuming a minimum allowed pressure head in the atmosphere, or an empirical reduction function (Black et al., 1969). The crop model inside SWAP is WOFOST (ALTERRA, 2004), simulating the daily growth of a specific crop, given the selected weather and soil data. For each simulation, users select specific boundary conditions, which consist of the crop calendar and the soil's water and nutrient status. Genetic Algorithm Genetic algorithms (GAs) are a search technique developed by Holland (1975) that uses the mechanisms of natural selection to search through decision space for optima solutions (Goldberg, 1989). The concept of chromosome and the three basic operations selection, crossover (mating), and mutation are the central part of GA. Each chromosome represents an encoding of information upon which GA will operate and consists of a string of bits (Binary 0/1). GA operates by maintaining a population of chromosomes. Each individual is assigned a fitness value based on a problem-specific evaluation function. GA rewards maximum fitness, so the evaluation function must be chosen so that its maximum corresponds to the desired value of the function to be optimized. At each iterative step called a generation, pairs of chromosomes are chosen for the crossover operation (is a form of mating which combines two chromosomes to produce two new chromosomes) and mutation (randomly changes the value of a single bit). Selection is a procedure to select a fixed number of chromosomes for the next generation according to their best fitness value. The genetic algorithm used in this study is a simple implementation of the above-mentioned processes of evolution but rather using the original binary-coded system implemented on similar optimizations by (Ines, 2002), it uses the real-coded genetic algorithm (Michalewicz, 1996). Which removes one layer of programming/processing that is the coding/decoding to-from binary bit strings. The parameters under optimization are the starting date of cropping, the time extent of cropping and the groundwater depth in 1st January and in 31st December. It is expected to use rice pixels with double cropping as a case study. The search domains for the dates of starting of cropping will require a non-overlapping restriction of about 90-100 days for soil preparation essentially. The time extent of the cropping season will be between 3 to 5 months. The groundwater level maybe ranging from 0 to 500cm depth but for the purpose of the case study it may be narrowed according to some general information about the area in order to improve the time efficiency for convergence. Consider C the cost function, having (x, y, d) parameters, x the longitude [0-180/E-W], y the latitude [0-90/N-S], d the date [yyyymmdd]. For the satellite data (i.e. Modis): d = [i,...,j], with i to j being the different satellite overpass dates, n is the total number of satellite dates being used.  The fitness of an individual having xy geographical characteristics will be the inverse of the cost function times the constraint aiming at minimizing the differences between SWAP simulation and target ETa,  3. Methodologies for Parallel or Distributed SWAP-GA To parallelize the SWAP-GA the tool used is MPI (PACS Training Group, 2004). MPI stands for "Message Passing Interface". MPI is a library of functions (in C) or subroutines (in FORTRAN) that one can insert into the source code to perform data communication between processors (Hoffman and Hargrove, 2000). A Master-Slave procedure is maintained to distribute the jobs inside a cluster. In Master-Slave terminology, there will be a front-end node (processor, called Master), which will communicate with users and command the other nodes (called slave or working nodes). Whenever any job submitted to cluster, first all available nodes or processors are ranked from "0" to available processors number. "0" is the rank for master node. Thereby, jobs will be distributed to slaves by Master node. 3.1 Parallel SWAP-GA with Distributed Population All populations will be distributed properly among available slaves by the Master computer. Slaves do the evaluation, generate the fitness and send back the population (with fitness) to the Master. A numerical experiment with parallel SWAP-GA with distributing population is presented in (Akhter S. et. al., 2005b) and (Akhter S. et. al., 2005c). 3.2 Parallel SWAP-GA with Distributed Pixel Pixels are evaluated sequentially inside a serial SWAP-GA program running. However, there is no internal relation between the pixels in the evaluation procedure. Thereby, each pixel can be evaluated separately in each computing node. This process is called "Distributed pixel" (Figure 1). At the very beginning of the running code, it is assumed that the master will partition the total image into several pixels and all separate pixels information will be in separate folders (inside master local Hard Disk) maintaining a specific format. All pixels will be distributed among the available slaves. First all pixels are equally distributed among slaves and the rest pixels are distributed to slaves sequentially through the rank 1…N slaves. At the running period each slave will just copy that specific folder or folders inside its own local Hard disk and evaluate total serial SWAP-GA procedure for that one pixel. It will eventually produce a total assimilation result for that pixel in a file in the local Hard Disk (Figure 2).  Figure 1: Domain Space of Distributed Pixel Methodology  Figure 2: Distributed Pixel Model Structure 4. Results  Figure 3: Distributed Pixel Method in Magi Cluster Figure 3 presents the time curves (increasing pixels and increased generation) for running SWAP-GA with distributed pixel method where the numbers of populations are fixed (8) and numbers of slaves are 3. In this figure, all curves (including serial) are linear and present approximately same values which representation a well parallelism behavior. A generic equation can be formed, where an expected time to evaluate (in Optima cluster and pixel/slave procedure) the SWAP-GA model with any combination of input parameters population numbers (5, 10, 15, 20, 25), generation numbers (10, 20, 30, 40,50) and pixel numbers (2, 4, 6, 8) are considered. Let the equation is  Here in equation 3:  In figure 4, it seems the equation generates time a little bit higher than the simulation time and average error margin is 6.5%.  Figure 4: Distributed Pixel: Increasing Pixel's Effect on Simulated and Equation Generate Time Curve 5. Conclusion Distributed pixels method provides a time optimization for agriculture monitoring with Remote Sensing data. Moreover, a generic equation is formed and its accuracy level is quite acceptable. With the help of this equation, it is possible to estimate the running time of SWAP-GA before implementing in clusters. In near future, the whole procedure for Remote Sensing image will be implemented, where million of pixels can be analyzed with the help of more optimized implementation method (combined of distributed pixel and distributed population). For that experiment purpose Grid computing technology may be considered, where Grid master node will distribute each pixel into available clusters and each cluster will execute SWAP-GA with distributing population method. It is believed that the whole parallel SWAP-GA will include one new part not only in the Grid-cluster computing arena but also in the Remote Sensing image analyzing field for agriculture monitoring. References
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