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SCRIPusers.ps in branches/2014/dev_r4650_UKMO14.5_SST_BIAS_CORRECTION/NEMOGCM/TOOLS/WEIGHTS/SCRIP1.4/doc – NEMO

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source: branches/2014/dev_r4650_UKMO14.5_SST_BIAS_CORRECTION/NEMOGCM/TOOLS/WEIGHTS/SCRIP1.4/doc/SCRIPusers.ps @ 5967

Last change on this file since 5967 was 5967, checked in by timgraham, 8 years ago
Reset keywords before merging with head of trunk
Property svn:keywords set to `Id`
File size: 207.5 KB

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1813	5251 y Fq(1)p eop
1814	%%Page: 2 4
1815	2 3 bop 324 1212 a Fn(Chapter)78 b(1)324 1627 y(In)-6
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1821	b(supp)s(orts)g(four)f(t)m(yp)s(es)i(of)e(remappings.)91
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1823	2441 y(remapping)37 b(sc)m(heme)j(that)f(is)f(ideally)f(suited)i(to)g
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1826	b(or)e(heat)h(\015ux\))g(m)m(ust)g(b)s(e)g(conserv)m(ed.)43
1827	b(The)25 b(sec-)324 2682 y(ond)30 b(t)m(yp)s(e)h(of)e(mapping)f(is)i(a)
1828	f(basic)h(bilinear)e(in)m(terp)s(olation)f(whic)m(h)j(has)h(b)s(een)f
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1830	(cal)e(bilinear)g(in)m(terp)s(olation.)67 b(A)41 b(third)f(metho)s(d)h
1831	(is)g(a)324 2922 y(bicubic)27 b(in)m(terp)s(olation)f(similar)f(to)j
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1833	(remap-)324 3043 y(ping)k(is)h(a)g(distance-w)m(eigh)m(ted)g(a)m(v)m
1834	(erage)h(of)f(nearest-neigh)m(b)s(or)g(p)s(oin)m(ts.)45
1835	b(The)34 b(bilinear)324 3163 y(and)39 b(bicubic)g(sc)m(hemes)i(can)f
1836	(only)e(b)s(e)i(used)g(with)f(logically-rectangular)c(grids;)42
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1838	(used)h(for)e(an)m(y)h(grid)e(in)h(spherical)g(co)s(ordinates.)470
1839	3404 y(SCRIP)i(is)e(a)m(v)-5 b(ailable)30 b(via)i(the)h(w)m(eb)g(at)324
1840	3524 y(h)m(ttp://climate.acl.lanl.go)m(v/soft)m(w)m(are/SCRIP/)324
1841	3645 y(NOTE:)g(This)g(lo)s(cation)d(has)j(c)m(hanged)h(since)f(the)g
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1843	(ho)m(w)g(to)f(compile)f(and)h(run)h(SCRIP)-8 b(,)44
1844	b(while)e(the)324 3885 y(follo)m(wing)30 b(sections)j(describ)s(e)g
1845	(the)g(remapping)e(metho)s(ds)i(in)f(more)g(detail.)1918
1846	5251 y(2)p eop
1847	%%Page: 3 5
1848	3 4 bop 324 1212 a Fn(Chapter)78 b(2)324 1627 y(Compiling)e(and)i
1849	(Running)324 2080 y Fq(The)44 b(distribution)e(\014le)h(is)g(a)g(gzipp)
1850	s(ed)h(tar\014le,)i(so)d(y)m(ou)i(m)m(ust)e(uncompress)i(the)f(\014le)
1851	324 2200 y(using)h(\\gunzip")g(and)h(then)g(extract)g(SCRIP)h(from)d
1852	(the)i(tar)f(\014le)g(using)g(\\tar)g(-xvf)324 2320 y(scrip1.4.tar".)69
1853	b(The)42 b(extraction)f(pro)s(cess)h(will)d(create)j(a)f(directory)h
1854	(called)e(SCRIP)324 2441 y(with)d(t)m(w)m(o)h(sub)s(directories)g
1855	(named)f(\\source")h(and)f(\\grids".)58 b(The)38 b(source)h(directory)
1856	324 2561 y(con)m(tains)d(all)f(the)i(source)g(\014les)g(and)f(the)h
1857	(mak)m(e\014le)g(for)f(building)e(the)j(pac)m(k)-5 b(age.)56
1858	b(The)324 2682 y(grids)37 b(directory)i(con)m(tains)f(some)g(sample)f
1859	(grid)g(\014les)h(and)h(routines)f(for)f(creating)h(or)324
1860	2802 y(con)m(v)m(erting)33 b(other)g(grid)e(\014les)i(to)f(the)h(prop)s
1861	(er)g(format.)324 3135 y Fm(2.1)160 b(Compiling)324 3354
1862	y Fq(In)40 b(order)g(to)g(compile)e(SCRIP)-8 b(,)41 b(y)m(ou)g(need)g
1863	(access)h(to)e(a)g(F)-8 b(ortran)39 b(90)g(compiler)f(and)324
1864	3474 y(a)44 b(netCDF)h(library)e(\(v)m(ersion)j(3)e(or)h(later\).)79
1865	b(In)45 b(the)g(source)h(directory)-8 b(,)48 b(y)m(ou)d(m)m(ust)324
1866	3595 y(edit)29 b(the)i(mak)m(e\014le)e(to)h(insert)g(the)g(appropriate)
1867	g(compiler)e(and)i(compiler)e(options)h(for)324 3715
1868	y(whatev)m(er)36 b(mac)m(hine)e(y)m(ou)h(happ)s(en)h(to)e(w)m(ork)h
1869	(on.)50 b(The)35 b(mak)m(e\014le)g(curren)m(tly)g(only)f(has)324
1870	3835 y(SGI)h(compiler)f(options.)53 b(In)36 b(addition,)f(y)m(ou)i(m)m
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1872	3956 y(to)g(\014nd)g(the)h(prop)s(er)f(netCDF)g(library)f(-)g(if)g
1873	(netCDF)i(is)e(in)h(y)m(our)g(default)g(path,)h(y)m(ou)324
1874	4076 y(ma)m(y)32 b(delete)h(the)g(path)g(altogether.)470
1875	4196 y(Once)d(the)f(mak)m(e\014le)f(has)h(b)s(een)h(edited)f(to)f
1876	(re\015ect)i(y)m(our)f(lo)s(cal)e(en)m(vironmen)m(t,)j(t)m(yp)s(e)324
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1878	b(default,)g(the)g(mak)m(e\014le)f(builds)g(t)m(w)m(o)h(executables)h
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1880	(executable)h(is)f(called)f(scrip)h(and)g(computes)324
1881	4558 y(all)27 b(the)i(necessary)i(w)m(eigh)m(ts)f(for)e(a)h(remapping.)
1882	41 b(The)30 b(second)g(executable)g(is)e(a)h(simple)324
1883	4678 y(test)k(co)s(de)g(scrip)p 946 4678 30 4 v 35 w(test)g(whic)m(h)g
1884	(will)e(test)i(the)g(w)m(eigh)m(ts)g(output)g(b)m(y)h(scrip.)1918
1885	5251 y(3)p eop
1886	%%Page: 4 6
1887	4 5 bop 1139 601 a Fq(Figure)32 b(2.1:)43 b(Required)33
1888	b(input)f(namelist.)324 829 y Fl(&remap_inputs)529 949
1889	y(num_maps)53 b(=)f(2)529 1070 y(grid1_file)i(=)d('grid_1_file_name')
1890	529 1190 y(grid2_file)j(=)d('grid_2_file_name')529 1310
1891	y(interp_file1)j(=)e('map_1_output_file_name')529 1431
1892	y(interp_file2)i(=)e('map_2_output_file_name')529 1551
1893	y(map1_name)i(=)d('name_for_mapping_1')529 1672 y(map2_name)j(=)d
1894	('name_for_mapping_2')529 1792 y(map_method)j(=)d('conservative')529
1895	1912 y(normalize_opt)k(=)c('frac')529 2033 y(output_opt)j(=)d('scrip')
1896	529 2153 y(restrict_type)k(=)c('latitude')529 2273 y(num_srch_bins)k(=)
1897	c(90)529 2394 y(luse_grid1_area)k(=)d(.false.)529 2514
1898	y(luse_grid2_area)j(=)d(.false.)324 2635 y(/)324 3016
1899	y Fk(2.1.1)136 b(Compile-time)47 b(P)l(arameters)324
1900	3201 y Fq(There)38 b(are)g(a)f(few)h(compile-time)c(parameters)j(that)g
1901	(can)h(b)s(e)g(c)m(hanged)g(b)s(efore)g(com-)324 3322
1902	y(piling)28 b(\(see)k(T)-8 b(able)31 b(2.1\).)42 b(F)-8
1903	b(or)30 b(the)i(most)e(part,)h(the)h(defaults)e(are)h(adequate,)i(but)e
1904	(y)m(ou)324 3442 y(ma)m(y)37 b(wish)g(to)g(c)m(hange)h(these)h(at)d
1905	(some)i(p)s(oin)m(t.)56 b(The)38 b(use)g(of)f(these)i(parameters)e
1906	(will)324 3562 y(b)s(ecome)32 b(clear)g(in)g(the)h(c)m(hapters)h
1907	(describing)e(the)h(remapping)f(algorithms.)324 3895
1908	y Fm(2.2)160 b(Running)324 4114 y Fq(Once)25 b(the)f(co)s(de)h(is)e
1909	(compiled,)h(a)g(few)h(input)f(\014les)g(are)g(needed.)42
1910	b(The)25 b(\014rst)g(is)f(a)f(namelist)324 4235 y(input)32
1911	b(\014le)g(and)h(the)g(other)f(t)m(w)m(o)i(required)f(\014les)f(are)h
1912	(grid)f(description)g(\014les.)324 4523 y Fk(2.2.1)136
1913	b(Namelist)47 b(Input)324 4708 y Fq(The)e(namelist)d(input)h(\014le)g
1914	(m)m(ust)h(b)s(e)g(called)f(scrip)p 2269 4708 30 4 v
1915	35 w(in)g(and)h(con)m(tain)g(a)f(namelist)f(as)324 4828
1916	y(sho)m(wn)34 b(in)d(Fig.)h(2.1.)1918 5251 y(4)p eop
1917	%%Page: 5 7
1918	5 6 bop 1155 1019 a Fq(T)-8 b(able)33 b(2.1:)43 b(Compile-time)29
1919	b(parameters)p 324 1050 3292 4 v 322 1170 4 121 v 374
1920	1134 a(Routine)p 1099 1170 V 439 w(P)m(arameter)p 1828
1921	1170 V 326 w(Default)p 2325 1170 V 140 w(Description)p
1922	3613 1170 V 322 1290 V 1099 1290 V 1151 1254 a(Name)p
1923	1828 1290 V 561 w(V)-8 b(alue)p 2325 1290 V 3613 1290
1924	V 324 1294 3292 4 v 322 1414 4 121 v 374 1378 a(remap)p
1925	646 1378 30 4 v 34 w(conserv.f)p 1099 1414 4 121 v 104
1926	w(north)p 1390 1378 30 4 v 35 w(thresh)p 1828 1414 4
1927	121 v 307 w(1.42)p 2325 1414 V 212 w(threshold)32 b(latitude)f(\(in)p
1928	3613 1414 V 322 1535 V 1099 1535 V 1828 1535 V 2325 1535
1929	V 2377 1498 a(radians\))g(ab)s(o)m(v)m(e)j(whic)m(h)f(a)p
1930	3613 1535 V 322 1655 V 1099 1655 V 1828 1655 V 2325 1655
1931	V 2377 1619 a(co)s(ordinate)e(transformation)p 3613 1655
1932	V 322 1775 V 1099 1775 V 1828 1775 V 2325 1775 V 2377
1933	1739 a(is)h(used)h(to)g(p)s(erform)p 3613 1775 V 322
1934	1896 V 1099 1896 V 1828 1896 V 2325 1896 V 2377 1860
1935	a(in)m(tersection)f(calculation)p 3613 1896 V 324 1899
1936	3292 4 v 322 2019 4 121 v 374 1983 a(remap)p 646 1983
1937	30 4 v 34 w(conserv.f)p 1099 2019 4 121 v 104 w(south)p
1938	1390 1983 30 4 v 35 w(thresh)p 1828 2019 4 121 v 291
1939	w(-2.00)p 2325 2019 V 195 w(same)g(for)g(south)h(p)s(ole)p
1940	3613 2019 V 324 2023 3292 4 v 322 2143 4 121 v 374 2107
1941	a(remap)p 646 2107 30 4 v 34 w(conserv.f)p 1099 2143
1942	4 121 v 104 w(max)p 1339 2107 30 4 v 34 w(subseg)p 1828
1943	2143 4 121 v 313 w(10000)p 2325 2143 V 176 w(maxim)m(um)d(n)m(um)m(b)s
1944	(er)j(of)f(sub-)p 3613 2143 V 322 2263 V 1099 2263 V
1945	1828 2263 V 2325 2263 V 2377 2227 a(segmen)m(ts)h(allo)m(w)m(ed)f(\(to)
1946	p 3613 2263 V 322 2384 V 1099 2384 V 1828 2384 V 2325
1947	2384 V 2377 2348 a(prev)m(en)m(t)i(in\014nite)e(lo)s(op\))p
1948	3613 2384 V 324 2387 3292 4 v 322 2508 4 121 v 374 2471
1949	a(remap)p 646 2471 30 4 v 34 w(bilinear.f)p 1099 2508
1950	4 121 v 98 w(max)p 1339 2471 30 4 v 34 w(iter)p 1828
1951	2508 4 121 v 491 w(100)p 2325 2508 V 225 w(max)g(n)m(um)m(b)s(er)h(of)f
1952	(iterations)p 3613 2508 V 322 2628 V 1099 2628 V 1828
1953	2628 V 2325 2628 V 2377 2592 a(to)g(determine)g(lo)s(cal)e(i,j)p
1954	3613 2628 V 324 2631 3292 4 v 322 2752 4 121 v 374 2716
1955	a(remap)p 646 2716 30 4 v 34 w(bilinear.f)p 1099 2752
1956	4 121 v 98 w(con)m(v)m(erge)p 1828 2752 V 364 w(1)22
1957	b Fo(\002)h Fq(10)2148 2679 y Fj(\000)p Fi(10)p 2325
1958	2752 V 2377 2716 a Fq(con)m(v)m(ergence)35 b(criterion)p
1959	3613 2752 V 322 2872 V 1099 2872 V 1828 2872 V 2325 2872
1960	V 2377 2836 a(for)d(bilinear)e(iteration)p 3613 2872
1961	V 324 2875 3292 4 v 322 2996 4 121 v 374 2960 a(remap)p
1962	646 2960 30 4 v 34 w(bicubic.f)p 1099 2996 4 121 v 116
1963	w(max)p 1339 2960 30 4 v 34 w(iter)p 1828 2996 4 121
1964	v 491 w(100)p 2325 2996 V 225 w(max)i(n)m(um)m(b)s(er)h(of)f
1965	(iterations)p 3613 2996 V 322 3116 V 1099 3116 V 1828
1966	3116 V 2325 3116 V 2377 3080 a(to)g(determine)g(lo)s(cal)e(i,j)p
1967	3613 3116 V 324 3119 3292 4 v 322 3240 4 121 v 374 3204
1968	a(remap)p 646 3204 30 4 v 34 w(bicubic.f)p 1099 3240
1969	4 121 v 116 w(con)m(v)m(erge)p 1828 3240 V 364 w(1)22
1970	b Fo(\002)h Fq(10)2148 3168 y Fj(\000)p Fi(10)p 2325
1971	3240 V 2377 3204 a Fq(con)m(v)m(ergence)35 b(criterion)p
1972	3613 3240 V 322 3360 V 1099 3360 V 1828 3360 V 2325 3360
1973	V 2377 3324 a(for)d(bicubic)g(iteration)p 3613 3360 V
1974	324 3363 3292 4 v 322 3484 4 121 v 374 3448 a(remap)p
1975	646 3448 30 4 v 34 w(dist)m(wgt.f)p 1099 3484 4 121 v
1976	108 w(n)m(um)p 1344 3448 30 4 v 35 w(neigh)m(b)s(ors)p
1977	1828 3484 4 121 v 274 w(4)p 2325 3484 V 274 w(n)m(um)m(b)s(er)h(of)f
1978	(nearest)p 3613 3484 V 322 3604 V 1099 3604 V 1828 3604
1979	V 2325 3604 V 2377 3568 a(neigh)m(b)s(ors)g(to)g(use)i(for)p
1980	3613 3604 V 322 3725 V 1099 3725 V 1828 3725 V 2325 3725
1981	V 2377 3689 a(distance-w)m(eigh)m(ted)f(a)m(v)m(erage)p
1982	3613 3725 V 324 3728 3292 4 v 322 3848 4 121 v 374 3812
1983	a(iounits.f)p 1099 3848 V 431 w(stdin)p 1828 3848 V 691
1984	w(5)p 2325 3848 V 274 w(I/O)f(unit)g(reserv)m(ed)j(for)p
1985	3613 3848 V 322 3969 V 1099 3969 V 1828 3969 V 2325 3969
1986	V 2377 3933 a(standard)e(input)p 3613 3969 V 324 3972
1987	3292 4 v 322 4092 4 121 v 374 4056 a(iounits.f)p 1099
1988	4092 V 431 w(stdout)p 1828 4092 V 632 w(6)p 2325 4092
1989	V 274 w(I/O)f(unit)g(reserv)m(ed)j(for)p 3613 4092 V
1990	322 4213 V 1099 4213 V 1828 4213 V 2325 4213 V 2377 4177
1991	a(standard)e(output)p 3613 4213 V 324 4216 3292 4 v 322
1992	4337 4 121 v 374 4300 a(iounits.f)p 1099 4337 V 431 w(stderr)p
1993	1828 4337 V 654 w(6)p 2325 4337 V 274 w(I/O)f(unit)g(reserv)m(ed)j(for)
1994	p 3613 4337 V 322 4457 V 1099 4457 V 1828 4457 V 2325
1995	4457 V 2377 4421 a(standard)e(error)f(output)p 3613 4457
1996	V 324 4460 3292 4 v 322 4581 4 121 v 374 4544 a(timers.f)p
1997	1099 4581 V 453 w(max)p 1339 4544 30 4 v 34 w(timers)p
1998	1828 4581 4 121 v 395 w(99)p 2325 4581 V 250 w(max)g(n)m(um)m(b)s(er)h
1999	(of)f(CPU)h(timers)p 3613 4581 V 324 4584 3292 4 v 1918
2000	5251 a(5)p eop
2001	%%Page: 6 8
2002	6 7 bop 470 548 a Fq(The)36 b(n)m(um)p 866 548 30 4 v
2003	35 w(maps)e(v)-5 b(ariable)34 b(determines)h(the)g(n)m(um)m(b)s(er)g
2004	(of)f(mappings)g(to)h(b)s(e)g(com-)324 668 y(puted.)41
2005	b(If)24 b(y)m(ou'd)h(lik)m(e)f(mappings)f(only)g(from)g(a)h(source)h
2006	(grid)e(\(grid)g(1\))h(to)g(a)g(destination)324 789 y(grid)29
2007	b(\(grid)g(2\),)i(then)g(n)m(um)p 1316 789 V 35 w(maps)f(should)g(b)s
2008	(e)g(set)h(to)f(one.)43 b(If)31 b(y)m(ou'd)g(also)e(lik)m(e)h(w)m(eigh)
2009	m(ts)324 909 y(for)i(a)f(remapping)h(in)f(the)i(opp)s(osite)e
2010	(direction)h(\(grid)f(2)h(to)g(grid)f(1\),)h(then)h(n)m(um)p
2011	3310 909 V 35 w(maps)324 1029 y(should)f(b)s(e)h(set)g(to)g(t)m(w)m(o.)
2012	470 1150 y(The)27 b(map)p 855 1150 V 34 w(metho)s(d)e(v)-5
2013	b(ariable)25 b(determines)g(the)i(metho)s(d)e(to)g(b)s(e)h(used)h(for)f
2014	(the)g(map-)324 1270 y(ping.)82 b(A)46 b(conserv)-5 b(ativ)m(e)47
2015	b(remapping)e(is)g(map)p 2099 1270 V 34 w(metho)s(d)h(`conserv)-5
2016	b(ativ)m(e';)53 b(a)46 b(bilinear)324 1391 y(mapping)20
2017	b(is)h(map)p 992 1391 V 35 w(metho)s(d)g(`bilinear';)i(a)f(distance-w)m
2018	(eigh)m(ted)g(a)m(v)m(erage)h(is)e(map)p 3254 1391 V
2019	34 w(metho)s(d)324 1511 y(`dist)m(wgt';)33 b(a)f(bicubic)g(mapping)f
2020	(is)h(map)p 1857 1511 V 35 w(metho)s(d)g(`bicubic'.)470
2021	1631 y(The)24 b(restrict)p 971 1631 V 36 w(t)m(yp)s(e)g(v)-5
2022	b(ariable)22 b(and)h(n)m(um)p 1941 1631 V 35 w(src)m(h)p
2023	2146 1631 V 37 w(bins)g(determines)h(ho)m(w)g(the)g(soft)m(w)m(are)324
2024	1752 y(restricts)g(the)g(range)g(of)f(grid)g(p)s(oin)m(ts)h(to)f(searc)
2025	m(h)i(to)f(a)m(v)m(oid)f(a)h(full)e Fh(N)2764 1716 y
2026	Fi(2)2828 1752 y Fq(searc)m(h.)42 b(There)25 b(are)324
2027	1872 y(curren)m(tly)34 b(t)m(w)m(o)h(options)e(for)g(restrict)p
2028	1731 1872 V 36 w(t)m(yp)s(e:)47 b(`latitude')32 b(and)i(`latlon'.)46
2029	b(The)34 b(\014rst)h(w)m(as)324 1993 y(used)j(in)f(all)e(previous)j(v)m
2030	(ersions)h(of)e(SCRIP)h(and)g(restricts)g(the)f(searc)m(h)i(b)m(y)g
2031	(dividing)324 2113 y(the)34 b(grid)f(p)s(oin)m(ts)h(in)m(to)g(n)m(um)p
2032	1383 2113 V 35 w(src)m(h)p 1588 2113 V 36 w(bins)g(latitude)f(bins.)48
2033	b(The)35 b(`latlon')d(c)m(hoice)j(divides)324 2233 y(the)g(spherical)f
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2274	%%Page: 11 13
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2295	%%Page: 12 14
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2375	%%Page: 13 15
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2419	%%Page: 14 16
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2438	Ff(k)1911 2944 y Fe(Z)53 b(Z)2056 3132 y Ff(A)2109 3144
2439	y Fd(k)2168 3061 y Fh(f)11 b(dA;)983 b Fq(\(3.1\))324
2440	3337 y(where)p 608 3259 77 4 v 36 w Fh(F)49 b Fq(is)34
2441	b(the)h(area-a)m(v)m(eraged)h(\015ux)g(and)f Fh(A)2068
2442	3352 y Ff(k)2145 3337 y Fq(is)g(the)g(area)g(of)f(cell)g
2443	Fh(k)s Fq(.)51 b(Because)36 b(the)324 3457 y(in)m(tegral)c(in)h
2444	(\(3.1\))g(is)g(o)m(v)m(er)i(the)f(area)g(of)f(the)h(destination)f
2445	(grid)g(cell,)g(only)g(those)h(cells)324 3578 y(on)27
2446	b(the)h(source)g(grid)e(that)h(are)g(co)m(v)m(ered)i(at)e(least)g
2447	(partly)g(b)m(y)h(the)f(destination)g(grid)f(cell)324
2448	3698 y(con)m(tribute)33 b(to)g(the)h(v)-5 b(alue)32 b(of)h(the)h
2449	(\015ux)g(on)f(the)g(destination)f(grid.)45 b(If)33 b(cell)f
2450	Fh(k)k Fq(o)m(v)m(erlaps)324 3818 y Fh(N)43 b Fq(cells)32
2451	b(on)g(the)h(source)h(grid,)d(the)i(remapping)f(can)h(b)s(e)f(written)h
2452	(as)p 1396 4029 V 1396 4107 a Fh(F)1472 4122 y Ff(k)1543
2453	4107 y Fq(=)1690 4040 y(1)p 1656 4084 116 4 v 1656 4176
2454	a Fh(A)1729 4191 y Ff(k)1833 3999 y(N)1805 4024 y Fe(X)1798
2455	4205 y Ff(n)p Fi(=1)1948 3990 y Fe(Z)54 b(Z)2094 4179
2456	y Ff(A)2147 4191 y Fd(nk)2244 4107 y Fh(f)2292 4122 y
2457	Ff(n)2339 4107 y Fh(dA;)871 b Fq(\(3.2\))324 4391 y(where)42
2458	b Fh(A)687 4406 y Ff(nk)814 4391 y Fq(is)f(the)g(area)g(of)g(the)g
2459	(source)h(grid)f(cell)f Fh(n)h Fq(co)m(v)m(ered)i(b)m(y)f(the)g
2460	(destination)324 4511 y(grid)37 b(cell)g Fh(k)s Fq(,)i(and)g
2461	Fh(f)1073 4526 y Ff(n)1158 4511 y Fq(is)e(the)i(lo)s(cal)d(v)-5
2462	b(alue)37 b(of)h(the)h(\015ux)f(in)g(the)g(source)h(grid)f(cell)f
2463	(\(see)324 4632 y(Figure)32 b(3.1\).)45 b(Note)33 b(that)g(\(3.2\))g
2464	(is)g(normalized)e(b)m(y)j(the)g(destination)e(area)h
2465	Fh(A)3242 4647 y Ff(k)3318 4632 y Fq(corre-)324 4752
2466	y(sp)s(onding)38 b(to)f(the)i(normalize)p 1463 4752 30
2467	4 v 33 w(opt)f(v)-5 b(alue)38 b(of)g(`destarea'.)61 b(The)39
2468	b(sum)f(of)g(the)h(w)m(eigh)m(ts)324 4872 y(for)i(a)h(destination)g
2469	(cell)f Fh(k)k Fq(in)c(this)h(case)h(w)m(ould)f(b)s(e)h(b)s(et)m(w)m
2470	(een)h(0)e(and)g(1)g(and)h(w)m(ould)324 4993 y(b)s(e)38
2471	b(the)g(area)f(fraction)g(if)f Fh(f)1359 5008 y Ff(n)1444
2472	4993 y Fq(w)m(ere)j(iden)m(tically)d(1)h(ev)m(erywhere)k(on)d(the)g
2473	(source)h(grid.)1894 5251 y(14)p eop
2474	%%Page: 15 17
2475	15 16 bop 324 548 a Fq(The)32 b(normalization)27 b(option)j(`fracarea')
2476	h(w)m(ould)g(actually)f(divide)g(b)m(y)i(the)g(area)f(of)f(the)324
2477	668 y(source)j(grid)f(o)m(v)m(erlapp)s(ed)h(b)m(y)h(cell)d
2478	Fh(k)s Fq(:)1680 846 y Ff(N)1651 871 y Fe(X)1645 1052
2479	y Ff(n)p Fi(=1)1794 837 y Fe(Z)54 b(Z)1940 1025 y Ff(A)1993
2480	1037 y Fd(nk)2090 954 y Fh(dA:)1120 b Fq(\(3.3\))324
2481	1234 y(F)-8 b(or)27 b(this)h(normalization)d(option,)j(remapping)f(a)i
2482	(function)e Fh(f)39 b Fq(whic)m(h)29 b(is)f(1)g(ev)m(erywhere)324
2483	1354 y(on)j(the)i(source)g(grid)d(w)m(ould)i(result)g(in)f(a)g
2484	(function)h Fh(F)45 b Fq(that)32 b(is)f(exactly)h(one)g(wherev)m(er)324
2485	1475 y(the)37 b(destination)f(grid)f(o)m(v)m(erlaps)j(a)e(non-mask)m
2486	(ed)i(source)g(grid)d(cell)h(and)h(zero)g(other-)324
2487	1595 y(wise.)70 b(A)41 b(normalization)c(option)j(of)h(`none')h(w)m
2488	(ould)f(result)g(in)g(the)h(actual)e(angular)324 1715
2489	y(area)32 b(participating)e(in)i(the)h(remapping.)470
2490	1836 y(Assuming)d Fh(f)964 1851 y Ff(n)1042 1836 y Fq(is)g(constan)m(t)
2491	i(across)g(a)e(source)i(grid)e(cell,)g(\(3.2\))g(w)m(ould)h(lead)f(to)g
2492	(the)324 1956 y(\014rst-order)39 b(area-w)m(eigh)m(ted)h(sc)m(hemes)h
2493	(used)g(in)e(curren)m(t)h(coupled)g(mo)s(dels.)63 b(A)39
2494	b(more)324 2077 y(accurate)33 b(form)e(of)h(the)h(remapping)f(is)g
2495	(obtained)g(b)m(y)h(using)1405 2293 y Fh(f)1453 2308
2496	y Ff(n)1528 2293 y Fq(=)p 1631 2214 59 4 v 27 w Fh(f)1690
2497	2317 y Ff(n)1759 2293 y Fq(+)22 b Fo(r)1940 2308 y Ff(n)1987
2498	2293 y Fh(f)33 b Fo(\001)22 b Fq(\()m Fh(~)-46 b(r)25
2499	b Fo(\000)19 b Fh(~)-46 b(r)2368 2308 y Ff(n)2415 2293
2500	y Fq(\))p Fh(;)881 b Fq(\(3.4\))324 2510 y(where)35 b
2501	Fo(r)690 2525 y Ff(n)737 2510 y Fh(f)45 b Fq(is)34 b(the)h(gradien)m(t)
2502	f(of)f(the)i(\015ux)g(in)f(cell)f Fh(n)h Fq(and)e Fh(~)-46
2503	b(r)2579 2525 y Ff(n)2660 2510 y Fq(is)34 b(the)h(cen)m(troid)f(of)g
2504	(cell)324 2630 y Fh(n)f Fq(de\014ned)h(b)m(y)1520 2789
2505	y Fh(~)-45 b(r)1568 2804 y Ff(n)1642 2789 y Fq(=)1791
2506	2722 y(1)p 1756 2766 121 4 v 1756 2858 a Fh(A)1829 2873
2507	y Ff(n)1902 2672 y Fe(Z)54 b(Z)2048 2861 y Ff(A)2101
2508	2869 y Fd(n)2161 2789 y Fh(~)-46 b(r)s(dA:)999 b Fq(\(3.5\))324
2509	3003 y(Suc)m(h)34 b(a)f(distribution)e(satis\014es)i(the)h(conserv)-5
2510	b(ation)33 b(constrain)m(t)g(and)g(is)f(equiv)-5 b(alen)m(t)33
2511	b(to)324 3123 y(the)i(\014rst)h(terms)f(of)g(a)g(T)-8
2512	b(a)m(ylor)35 b(series)h(expansion)f(of)g Fh(f)46 b Fq(around)32
2513	b Fh(~)-46 b(r)2783 3138 y Ff(n)2830 3123 y Fq(.)52 b(The)36
2514	b(remapping)324 3243 y(is)h(th)m(us)h(second-order)h(accurate)f(if)e
2515	Fo(r)1793 3258 y Ff(n)1840 3243 y Fh(f)49 b Fq(is)37
2516	b(at)g(least)g(a)g(\014rst-order)h(appro)m(ximation)324
2517	3364 y(to)32 b(the)h(gradien)m(t.)470 3484 y(The)h(remapping)d(can)i
2518	(no)m(w)g(b)s(e)g(expanded)h(in)e(spherical)g(co)s(ordinates)g(as)p
2519	775 3691 77 4 v 775 3769 a Fh(F)852 3784 y Ff(k)922 3769
2520	y Fq(=)1061 3662 y Ff(N)1032 3686 y Fe(X)1026 3868 y
2521	Ff(n)p Fi(=1)1176 3623 y Fe(")p 1224 3690 59 4 v 146
2522	x Fh(f)1283 3793 y Ff(n)1330 3769 y Fh(w)1400 3784 y
2523	Fi(1)p Ff(nk)1542 3769 y Fq(+)1640 3623 y Fe( )1716 3702
2524	y Fh(@)5 b(f)p 1716 3746 116 4 v 1721 3838 a(@)g(\022)1842
2525	3623 y Fe(!)1907 3873 y Ff(n)1971 3769 y Fh(w)2041 3784
2526	y Fi(2)p Ff(nk)2184 3769 y Fq(+)2282 3623 y Fe( )2431
2527	3702 y Fq(1)p 2357 3746 196 4 v 2357 3838 a(cos)17 b
2528	Fh(\022)2573 3702 y(@)5 b(f)p 2573 3746 116 4 v 2573
2529	3838 a(@)g(\036)2698 3623 y Fe(!)2764 3873 y Ff(n)2827
2530	3769 y Fh(w)2897 3784 y Fi(3)p Ff(nk)3018 3623 y Fe(#)3083
2531	3769 y Fh(;)251 b Fq(\(3.6\))324 4050 y(where)34 b Fh(\022)h
2532	Fq(is)d(latitude,)g Fh(\036)g Fq(is)g(longitude)f(and)i(the)g(three)g
2533	(remapping)e(w)m(eigh)m(ts)j(are)1474 4305 y Fh(w)1544
2534	4320 y Fi(1)p Ff(nk)1692 4305 y Fq(=)1839 4238 y(1)p
2535	1806 4282 V 1806 4373 a Fh(A)1879 4388 y Ff(k)1948 4188
2536	y Fe(Z)54 b(Z)2094 4377 y Ff(A)2147 4389 y Fd(nk)2244
2537	4305 y Fh(dA;)966 b Fq(\(3.7\))1012 4721 y Fh(w)1082
2538	4736 y Fi(2)p Ff(nk)1285 4721 y Fq(=)1487 4653 y(1)p
2539	1454 4697 V 1454 4789 a Fh(A)1527 4804 y Ff(k)1596 4603
2540	y Fe(Z)54 b(Z)1742 4792 y Ff(A)1795 4804 y Fd(nk)1876
2541	4721 y Fq(\()p Fh(\022)25 b Fo(\000)d Fh(\022)2128 4736
2542	y Ff(n)2176 4721 y Fq(\))p Fh(dA)1285 4969 y Fq(=)1487
2543	4901 y(1)p 1454 4945 V 1454 5037 a Fh(A)1527 5052 y Ff(k)1596
2544	4851 y Fe(Z)54 b(Z)1742 5040 y Ff(A)1795 5052 y Fd(nk)1892
2545	4969 y Fh(\022)s(dA)22 b Fo(\000)2196 4901 y Fh(w)2266
2546	4916 y Fi(1)p Ff(nk)p 2196 4945 191 4 v 2231 5037 a Fh(A)2304
2547	5052 y Ff(n)2413 4851 y Fe(Z)54 b(Z)2559 5040 y Ff(A)2612
2548	5048 y Fd(n)2675 4969 y Fh(\022)s(dA;)487 b Fq(\(3.8\))1894
2549	5251 y(15)p eop
2550	%%Page: 16 18
2551	16 17 bop 324 548 a Fq(and)790 787 y Fh(w)860 802 y Fi(3)p
2552	Ff(nk)1064 787 y Fq(=)1266 720 y(1)p 1232 764 116 4 v
2553	1232 856 a Fh(A)1305 871 y Ff(k)1375 670 y Fe(Z)53 b(Z)1521
2554	859 y Ff(A)1574 871 y Fd(nk)1671 787 y Fq(cos)17 b Fh(\022)s
2555	Fq(\()p Fh(\036)22 b Fo(\000)g Fh(\036)2141 802 y Ff(n)2188
2556	787 y Fq(\))p Fh(dA)1064 1036 y Fq(=)1266 968 y(1)p 1232
2557	1012 V 1232 1104 a Fh(A)1305 1119 y Ff(k)1375 918 y Fe(Z)53
2558	b(Z)1521 1107 y Ff(A)1574 1119 y Fd(nk)1671 1036 y Fh(\036)17
2559	b Fq(cos)f Fh(\022)s(dA)22 b Fo(\000)2196 968 y Fh(w)2266
2560	983 y Fi(1)p Ff(nk)p 2196 1012 191 4 v 2231 1104 a Fh(A)2304
2561	1119 y Ff(n)2413 918 y Fe(Z)54 b(Z)2559 1107 y Ff(A)2612
2562	1115 y Fd(n)2675 1036 y Fh(\036)17 b Fq(cos)f Fh(\022)s(dA:)266
2563	b Fq(\(3.9\))324 1301 y(Again,)46 b(if)d(the)i(gradien)m(t)e(is)h
2564	(zero,)k(\(3.6\))43 b(reduces)j(to)e(a)g(\014rst-order)g(area-w)m(eigh)
2565	m(ted)324 1422 y(remapping.)470 1542 y(The)d(area)e(in)m(tegrals)g(in)g
2566	(equations)g(\(3.7\){\(3.9\))g(are)h(computed)f(b)m(y)i(con)m(v)m
2567	(erting)324 1663 y(the)j(area)g(in)m(tegrals)f(in)m(to)h(line)f(in)m
2568	(tegrals)g(using)g(the)i(div)m(ergence)h(theorem.)78
2569	b(Com-)324 1783 y(puting)31 b(line)g(in)m(tegrals)h(around)g(the)h(o)m
2570	(v)m(erlap)f(regions)g(is)g(m)m(uc)m(h)h(simpler;)d(one)j(simply)324
2571	1903 y(in)m(tegrates)d(\014rst)h(around)f(ev)m(ery)i(grid)e(cell)f(on)h
2572	(the)h(source)g(grid,)f(k)m(eeping)h(trac)m(k)g(of)f(in-)324
2573	2024 y(tersections)i(with)e(destination)g(grid)g(lines,)g(and)h(then)h
2574	(one)f(in)m(tegrates)g(around)g(ev)m(ery)324 2144 y(grid)d(cell)f(on)i
2575	(the)g(destination)f(grid)g(in)g(a)g(similar)e(manner.)41
2576	b(After)29 b(the)h(sw)m(eep)g(of)f(eac)m(h)324 2265 y(grid,)i(all)g(o)m
2577	(v)m(erlap)i(regions)f(ha)m(v)m(e)i(b)s(een)f(in)m(tegrated.)470
2578	2385 y(Cho)s(osing)e(appropriate)g(functions)h(for)f(the)h(div)m
2579	(ergence,)i(the)e(in)m(tegrals)e(in)h(equa-)324 2505
2580	y(tions)h(\(3.7\){\(3.9\))f(b)s(ecome)1363 2638 y Fe(Z)54
2581	b(Z)1509 2827 y Ff(A)1562 2839 y Fd(nk)1659 2755 y Fh(dA)28
2582	b Fq(=)1914 2638 y Fe(I)1960 2827 y Ff(C)2010 2839 y
2583	Fd(nk)2108 2755 y Fo(\000)17 b Fq(sin)f Fh(\022)s(d\036;)790
2584	b Fq(\(3.10\))1130 2946 y Fe(Z)53 b(Z)1275 3135 y Ff(A)1328
2585	3147 y Fd(nk)1425 3064 y Fh(\022)s(dA)28 b Fq(=)1729
2586	2946 y Fe(I)1775 3135 y Ff(C)1825 3147 y Fd(nk)1906 3064
2587	y Fq([)p Fo(\000)17 b Fq(cos)g Fh(\022)25 b Fo(\000)e
2588	Fh(\022)d Fq(sin)c Fh(\022)s Fq(])p Fh(d\036;)556 b Fq(\(3.11\))981
2589	3229 y Fe(Z)53 b(Z)1127 3417 y Ff(A)1180 3429 y Fd(nk)1277
2590	3346 y Fh(\036)17 b Fq(cos)f Fh(\022)s(dA)28 b Fq(=)1801
2591	3229 y Fe(I)1847 3417 y Ff(C)1897 3429 y Fd(nk)1995 3346
2592	y Fo(\000)2082 3278 y Fh(\036)p 2082 3322 58 4 v 2086
2593	3414 a Fq(2)2150 3346 y([sin)17 b Fh(\022)i Fq(cos)f
2594	Fh(\022)25 b Fq(+)d Fh(\022)s Fq(])p Fh(d\036;)407 b
2595	Fq(\(3.12\))324 3560 y(where)36 b Fh(C)678 3575 y Ff(nk)799
2596	3560 y Fq(is)f(the)h(coun)m(terclo)s(c)m(kwise)h(path)e(around)h(the)g
2597	(region)e Fh(A)2920 3575 y Ff(nk)3006 3560 y Fq(.)52
2598	b(Computing)324 3681 y(these)d(three)f(line)e(in)m(tegrals)g(during)h
2599	(the)h(sw)m(eeps)i(of)d(eac)m(h)h(grid)f(pro)m(vides)h(all)d(the)324
2600	3801 y(information)29 b(necessary)35 b(for)d(computing)f(the)i
2601	(remapping)f(w)m(eigh)m(ts.)324 4134 y Fm(3.1)160 b(Searc)l(h)53
2602	b(algorithms)324 4353 y Fq(As)22 b(men)m(tioned)g(in)g(the)g(previous)h
2603	(section,)h(the)f(algorithm)c(for)i(computing)g(the)i(remap-)324
2604	4473 y(ping)h(w)m(eigh)m(ts)i(is)f(relativ)m(ely)f(simple.)39
2605	b(The)26 b(pro)s(cess)h(amoun)m(ts)e(to)g(\014nding)f(the)i(lo)s
2606	(cation)324 4594 y(of)k(the)h(endp)s(oin)m(t)g(of)f(a)h(segmen)m(t)g
2607	(and)g(then)h(\014nding)e(the)h(next)h(in)m(tersection)f(with)f(the)324
2608	4714 y(other)35 b(grid.)50 b(The)35 b(line)f(in)m(tegrals)g(are)h(then)
2609	h(computed)f(and)g(summed)g(according)f(to)324 4834 y(whic)m(h)k(grid)g
2610	(cells)f(are)h(asso)s(ciated)g(with)g(that)g(particular)e(subsegmen)m
2611	(t.)62 b(The)39 b(most)324 4955 y(time-consuming)h(p)s(ortion)g(of)i
2612	(the)h(algorithm)c(is)j(\014nding)g(whic)m(h)h(cell)e(on)h(one)h(grid)
2613	1894 5251 y(16)p eop
2614	%%Page: 17 19
2615	17 18 bop 324 956 a Fq(Figure)39 b(3.1:)58 b(An)40 b(example)g(of)g(a)f
2616	(triangular)f(destination)h(grid)g(cell)g Fh(k)k Fq(o)m(v)m(erlapping)
2617	324 1077 y(a)k(quadrilateral)e(source)j(grid.)86 b(The)49
2618	b(region)d Fh(A)2203 1092 y Ff(k)r(n)2336 1077 y Fq(is)g(where)j(cell)d
2619	Fh(k)k Fq(o)m(v)m(erlaps)e(the)324 1197 y(quadrilateral)42
2620	b(cell)h Fh(n)p Fq(.)78 b(V)-8 b(ectors)45 b(used)g(b)m(y)h(searc)m(h)f
2621	(and)f(in)m(tersection)g(routines)h(are)324 1317 y(also)31
2622	b(lab)s(elled.)1154 4646 y Fc(\010)1237 4605 y(\010)1320
2623	4563 y(\010)1403 4522 y(\010)1486 4480 y(\010)1569 4439
2624	y(\010)1652 4397 y(\010)1735 4356 y(\010)1818 4314 y(\010)1901
2625	4273 y(\010)1984 4231 y(\010)2067 4190 y(\010)2150 4148
2626	y(\010)2233 4107 y(\010)2316 4065 y(\010)2399 4024 y(\010)2482
2627	3982 y(\010)2565 3941 y(\010)2648 3899 y(\010)2731 3858
2628	y(\010)2814 3816 y(\010)2897 3775 y(\010)2980 3733 y(\010)3064
2629	3692 y(\010)3147 3650 y(\010)3230 3609 y(\010)3313 3567
2630	y(\010)3396 3526 y(\010)3479 3484 y(\010)3562 3443 y(\010)739
2631	3816 y(\010)822 3775 y(\010)905 3733 y(\010)988 3692
2632	y(\010)1071 3650 y(\010)1154 3609 y(\010)1237 3567 y(\010)1320
2633	3526 y(\010)1403 3484 y(\010)1486 3443 y(\010)1569 3401
2634	y(\010)1652 3360 y(\010)1735 3318 y(\010)1818 3277 y(\010)1901
2635	3235 y(\010)1984 3194 y(\010)2067 3152 y(\010)2150 3111
2636	y(\010)2233 3069 y(\010)2316 3028 y(\010)2399 2986 y(\010)2482
2637	2945 y(\010)2565 2903 y(\010)2648 2861 y(\010)2731 2820
2638	y(\010)2814 2778 y(\010)2897 2737 y(\010)2980 2695 y(\010)3064
2639	2654 y(\010)3147 2612 y(\010)324 2986 y(\010)407 2945
2640	y(\010)490 2903 y(\010)573 2861 y(\010)656 2820 y(\010)739
2641	2778 y(\010)822 2737 y(\010)905 2695 y(\010)988 2654
2642	y(\010)1071 2612 y(\010)1154 2571 y(\010)1237 2529 y(\010)1320
2643	2488 y(\010)1403 2446 y(\010)1486 2405 y(\010)1569 2363
2644	y(\010)1652 2322 y(\010)1735 2280 y(\010)1818 2239 y(\010)1901
2645	2197 y(\010)1984 2156 y(\010)2067 2114 y(\010)2150 2073
2646	y(\010)2233 2031 y(\010)2316 1990 y(\010)2399 1948 y(\010)2482
2647	1907 y(\010)2565 1865 y(\010)2648 1824 y(\010)2731 1782
2648	y(\010)324 3069 y(A)365 3152 y(A)407 3235 y(A)448 3318
2649	y(A)490 3401 y(A)531 3484 y(A)573 3567 y(A)614 3650 y(A)656
2650	3733 y(A)697 3816 y(A)739 3899 y(A)780 3982 y(A)822 4065
2651	y(A)863 4148 y(A)905 4231 y(A)946 4314 y(A)988 4397 y(A)1029
2652	4480 y(A)1071 4563 y(A)1112 4646 y(A)1154 2654 y(A)1196
2653	2737 y(A)1237 2820 y(A)1279 2903 y(A)1320 2986 y(A)1362
2654	3069 y(A)1403 3152 y(A)1445 3235 y(A)1486 3318 y(A)1528
2655	3401 y(A)1569 3484 y(A)1611 3567 y(A)1652 3650 y(A)1694
2656	3733 y(A)1735 3816 y(A)1777 3899 y(A)1818 3982 y(A)1860
2657	4065 y(A)1901 4148 y(A)1943 4231 y(A)1984 2239 y(A)2026
2658	2322 y(A)2067 2405 y(A)2109 2488 y(A)2150 2571 y(A)2192
2659	2654 y(A)2233 2737 y(A)2275 2820 y(A)2316 2903 y(A)2358
2660	2986 y(A)2399 3069 y(A)2441 3152 y(A)2482 3235 y(A)2524
2661	3318 y(A)2565 3401 y(A)2607 3484 y(A)2648 3567 y(A)2690
2662	3650 y(A)2731 3733 y(A)2773 3816 y(A)2814 1824 y(A)2856
2663	1907 y(A)2897 1990 y(A)2939 2073 y(A)2980 2156 y(A)3022
2664	2239 y(A)3064 2322 y(A)3105 2405 y(A)3147 2488 y(A)3188
2665	2571 y(A)3230 2654 y(A)3271 2737 y(A)3313 2820 y(A)3354
2666	2903 y(A)3396 2986 y(A)3437 3069 y(A)3479 3152 y(A)3520
2667	3235 y(A)3562 3318 y(A)3603 3401 y(A)p 739 3610 1661
2668	4 v 2399 3609 a(\003)2420 3526 y(\003)2441 3443 y(\003)2462
2669	3360 y(\003)2482 3277 y(\003)2503 3194 y(\003)2524 3111
2670	y(\003)2545 3028 y(\003)2565 2945 y(\003)2586 2861 y(\003)2607
2671	2778 y(\003)2628 2695 y(\003)2648 2612 y(\003)2669 2529
2672	y(\003)2690 2446 y(\003)2711 2363 y(\003)2648 2336 y
2673	Fb(\021)2565 2391 y(\021)2482 2446 y(\021)2399 2502 y(\021)2316
2674	2557 y(\021)2233 2612 y(\021)2150 2668 y(\021)2067 2723
2675	y(\021)1984 2778 y(\021)1901 2834 y(\021)1818 2889 y(\021)1735
2676	2945 y(\021)1652 3000 y(\021)1569 3055 y(\021)1486 3111
2677	y(\021)1403 3166 y(\021)1320 3221 y(\021)1237 3277 y(\021)1154
2678	3332 y(\021)1071 3387 y(\021)988 3443 y(\021)905 3498
2679	y(\021)822 3553 y(\021)739 3609 y(\021)-83 b(+)1984 2239
2680	y(A)2026 2322 y(A)2067 2405 y(A)2109 2488 y(A)2150 2571
2681	y(A)2192 2654 y(A)2233 2737 y(A)2275 2820 y(A)2316 2903
2682	y(A)2358 2986 y(A)-42 b(U)1984 2177 y(X)2067 2197 y(X)2150
2683	2218 y(X)2233 2239 y(X)2316 2260 y(X)2399 2280 y(X)2482
2684	2301 y(X)2565 2322 y(X)2648 2343 y(X)-83 b(z)2396 2197
2685	y Fh(~)-46 b(r)2443 2212 y Fi(1)p Ff(b)1939 2405 y Fh(~)h(r)1987
2686	2420 y Fi(12)1773 2778 y Fh(~)g(r)1821 2793 y Ff(be)1735
2687	2073 y Fq(\()p Fh(\022)1818 2088 y Fi(1)1858 2073 y Fh(;)17
2688	b(\036)1960 2088 y Fi(1)1999 2073 y Fq(\))2441 2986 y(\()p
2689	Fh(\022)2524 3001 y Fi(2)2564 2986 y Fh(;)g(\036)2666
2690	3001 y Fi(2)2705 2986 y Fq(\))2814 2280 y(\()p Fh(\022)2897
2691	2295 y Ff(b)2932 2280 y Fh(;)g(\036)3034 2295 y Ff(b)3068
2692	2280 y Fq(\))407 3609 y(\()p Fh(\022)490 3624 y Ff(e)527
2693	3609 y Fh(;)g(\036)629 3624 y Ff(e)665 3609 y Fq(\))1984
2694	2156 y Fa(s)2399 2986 y(s)2731 2280 y(s)739 3609 y(s)2192
2695	2778 y Fq(Cell)31 b Fh(k)2399 3816 y Fq(Cell)h Fh(n)1984
2696	3401 y(A)2057 3416 y Ff(k)r(n)1894 5251 y Fq(17)p eop
2697	%%Page: 18 20
2698	18 19 bop 324 548 a Fq(con)m(tains)42 b(an)g(endp)s(oin)m(t)f(from)g
2699	(the)h(other)g(grid.)71 b(Optimal)39 b(searc)m(h)k(algorithms)c(can)324
2700	668 y(b)s(e)44 b(written)f(when)i(the)f(grid)f(is)g(w)m(ell)g
2701	(structured)i(and)f(regular.)76 b(Ho)m(w)m(ev)m(er,)49
2702	b(if)42 b(one)324 789 y(requires)37 b(a)f(searc)m(h)h(algorithm)c(that)
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2706	(address)324 1029 y(is)f(assigned)g(to)g(one)g(or)g(more)g(latitude)f
2707	(bins.)42 b(When)31 b(the)g(searc)m(h)h(b)s(egins,)e(only)g(those)324
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2709	h(the)g(searc)m(h)h(p)s(oin)m(t)e(are)h(used.)63 b(The)324
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2715	(restricts)g(the)g(searc)m(h)g(to)f(a)g(small)e(n)m(um)m(b)s(er)j(of)
2716	324 1631 y(cells.)470 1752 y(Once)40 b(the)g(searc)m(h)h(has)f(b)s(een)
2717	g(restricted,)i(a)e(robust)g(algorithm)c(that)j(w)m(orks)i(for)324
2718	1872 y(most)32 b(cases)j(is)e(a)g(cross-pro)s(duct)h(test.)46
2719	b(In)33 b(this)g(test,)h(a)f(cross)h(pro)s(duct)g(is)e(computed)324
2720	1993 y(b)s(et)m(w)m(een)47 b(the)e(v)m(ector)h(corresp)s(onding)f(to)g
2721	(a)f(cell)g(side)h(\()m Fh(~)-46 b(r)2538 2008 y Fi(12)2657
2722	1993 y Fq(in)45 b(Figure)e(3.1\))i(and)g(a)324 2113 y(v)m(ector)30
2723	b(extending)f(from)e(the)j(b)s(eginning)d(of)h(the)h(cell)f(side)h(to)f
2724	(the)h(searc)m(h)h(p)s(oin)m(t)e(\()m Fh(~)-46 b(r)3427
2725	2128 y Fi(1)p Ff(b)3497 2113 y Fq(\).)324 2233 y(If)1659
2726	2354 y Fh(~)g(r)1706 2369 y Fi(12)1803 2354 y Fo(\002)19
2727	b Fh(~)-45 b(r)1947 2369 y Fi(1)p Ff(b)2044 2354 y Fh(>)27
2728	b Fq(0)p Fh(;)1089 b Fq(\(3.13\))324 2514 y(the)38 b(p)s(oin)m(t)f
2729	(lies)g(to)h(the)g(left)g(of)f(the)i(cell)d(side.)60
2730	b(If)38 b(\(3.13\))g(holds)f(for)h(ev)m(ery)i(cell)c(side,)324
2731	2635 y(the)d(p)s(oin)m(t)e(is)h(enclosed)h(b)m(y)g(the)g(cell.)42
2732	b(This)33 b(test)g(is)e(not)i(completely)e(robust)h(and)h(will)324
2733	2755 y(fail)d(for)i(grid)g(cells)g(that)g(are)g(non-con)m(v)m(ex.)324
2734	3083 y Fm(3.2)160 b(In)l(tersections)324 3302 y Fq(Once)34
2735	b(the)h(lo)s(cation)c(of)j(an)g(initial)c(endp)s(oin)m(t)k(is)f(found,)
2736	i(it)d(is)i(necessary)i(to)e(c)m(hec)m(k)i(to)324 3423
2737	y(see)27 b(if)e(the)h(segmen)m(t)g(in)m(tersects)i(with)d(the)h(cell)f
2738	(side.)41 b(If)26 b(the)h(segmen)m(t)f(is)f(parametrized)324
2739	3543 y(as)1461 3731 y Fh(\022)87 b Fq(=)c Fh(\022)1797
2740	3746 y Ff(b)1854 3731 y Fq(+)22 b Fh(s)1998 3746 y Fi(1)2037
2741	3731 y Fq(\()p Fh(\022)2120 3746 y Ff(e)2179 3731 y Fo(\000)h
2742	Fh(\022)2324 3746 y Ff(b)2359 3731 y Fq(\))1452 3877
2743	y Fh(\036)83 b Fq(=)g Fh(\036)1810 3892 y Ff(b)1866 3877
2744	y Fq(+)22 b Fh(s)2010 3892 y Fi(1)2049 3877 y Fq(\()p
2745	Fh(\036)2145 3892 y Ff(e)2204 3877 y Fo(\000)h Fh(\036)2362
2746	3892 y Ff(b)2396 3877 y Fq(\))878 b(\(3.14\))324 4065
2747	y(and)32 b(the)h(cell)f(side)h(as)1442 4253 y Fh(\022)86
2748	b Fq(=)d Fh(\022)1777 4268 y Fi(1)1839 4253 y Fq(+)22
2749	b Fh(s)1983 4268 y Fi(2)2022 4253 y Fq(\()p Fh(\022)2105
2750	4268 y Fi(2)2167 4253 y Fo(\000)h Fh(\022)2312 4268 y
2751	Fi(1)2352 4253 y Fq(\))1432 4399 y Fh(\036)83 b Fq(=)g
2752	Fh(\036)1790 4414 y Fi(1)1851 4399 y Fq(+)22 b Fh(s)1995
2753	4414 y Fi(2)2034 4399 y Fq(\()p Fh(\036)2130 4414 y Fi(2)2192
2754	4399 y Fo(\000)g Fh(\036)2349 4414 y Fi(1)2388 4399 y
2755	Fq(\))p Fh(;)859 b Fq(\(3.15\))324 4587 y(where)39 b
2756	Fh(\022)656 4602 y Fi(1)696 4587 y Fh(;)17 b(\036)798
2757	4602 y Fi(1)836 4587 y Fh(;)g(\022)925 4602 y Fi(2)965
2758	4587 y Fh(;)g(\036)1067 4602 y Fi(2)1106 4587 y Fh(;)g(\022)1195
2759	4602 y Ff(b)1229 4587 y Fh(;)38 b Fq(and)g Fh(\022)1534
2760	4602 y Ff(e)1609 4587 y Fq(are)g(endp)s(oin)m(ts)g(as)g(sho)m(wn)h(in)d
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2762	m(o)g(lines)e(o)s(ccurs)j(when)f Fh(\022)i Fq(and)e Fh(\036)f
2763	Fq(are)g(equal.)43 b(The)31 b(linear)e(system)933 4806
2764	y Fe(")1035 4891 y Fq(\()p Fh(\022)1118 4906 y Ff(e)1178
2765	4891 y Fo(\000)22 b Fh(\022)1322 4906 y Ff(b)1357 4891
2766	y Fq(\))108 b(\()p Fh(\022)1586 4906 y Fi(1)1648 4891
2767	y Fo(\000)22 b Fh(\022)1792 4906 y Fi(2)1832 4891 y Fq(\))1023
2768	5012 y(\()p Fh(\036)1119 5027 y Ff(e)1178 5012 y Fo(\000)g
2769	Fh(\036)1335 5027 y Ff(b)1370 5012 y Fq(\))82 b(\()p
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2771	5027 y Fi(2)1845 5012 y Fq(\))1924 4806 y Fe(#)17 b(")2079
2772	4891 y Fh(s)2125 4906 y Fi(1)2079 5012 y Fh(s)2125 5027
2773	y Fi(2)2206 4806 y Fe(#)2282 4952 y Fq(=)2385 4806 y
2774	Fe(")2488 4891 y Fq(\()p Fh(\022)2571 4906 y Fi(1)2633
2775	4891 y Fo(\000)22 b Fh(\022)2777 4906 y Ff(b)2812 4891
2776	y Fq(\))2475 5012 y(\()p Fh(\036)2571 5027 y Fi(1)2633
2777	5012 y Fo(\000)g Fh(\036)2790 5027 y Ff(b)2824 5012 y
2778	Fq(\))2904 4806 y Fe(#)3312 4952 y Fq(\(3.16\))1894 5251
2779	y(18)p eop
2780	%%Page: 19 21
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2784	b(If)34 b Fh(s)3211 563 y Fi(1)3285 548 y Fq(and)g Fh(s)3522
2785	563 y Fi(2)324 668 y Fq(are)e(b)s(et)m(w)m(een)j(zero)e(and)g(one,)g
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2793	y(an)j(endp)s(oin)m(t.)324 1483 y Fm(3.3)160 b(Coincidences)324
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2799	b(can)g(b)s(e)g(detected)h(when)g(computing)e(cross)324
2800	2063 y(pro)s(ducts)23 b(for)f(the)i(searc)m(h)g(algorithm)19
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2802	(duct)f(is)f(zero)324 2183 y(in)g(this)h(case,)j(the)e(endp)s(oin)m(t)f
2803	(lies)f(on)h(the)h(cell)e(side.)40 b(A)23 b(second)i(cross)f(pro)s
2804	(duct)g(b)s(et)m(w)m(een)324 2304 y(the)31 b(line)e(segmen)m(t)i(and)g
2805	(the)g(cell)e(side)i(can)f(then)i(b)s(e)e(computed.)43
2806	b(If)31 b(the)g(second)h(cross)324 2424 y(pro)s(duct)38
2807	b(is)f(also)g(zero,)i(the)f(lines)f(are)h(coinciden)m(t.)59
2808	b(Once)38 b(a)g(coincidence)g(has)g(b)s(een)324 2544
2809	y(detected,)29 b(the)e(con)m(tribution)e(of)h(the)h(coinciden)m(t)f
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2817	3457 y(line)26 b(on)i(the)h(sphere,)h(and)e(this)g(branc)m(h)h(cut)f
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2823	3818 y(alw)m(a)m(ys)c(c)m(hec)m(k)h(to)f(mak)m(e)f(sure)h(the)g
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2825	b(as)i(the)g(source)324 3939 y(grid)h(cell)h(cen)m(ter.)470
2826	4059 y(Another)i(problem)e(with)h(computing)f(w)m(eigh)m(ts)i(in)e
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2828	b(of)g(the)h(p)s(ole.)81 b(First,)48 b(note)e(that)f(although)f(the)i
2829	(p)s(ole)f(is)g(ph)m(ysically)g(a)324 4300 y(p)s(oin)m(t,)31
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2831	f(nonzero)h(con)m(tribution)324 4420 y(to)27 b(the)h(w)m(eigh)m(t)f(in)
2832	m(tegrals.)41 b(If)27 b(a)g(grid)f(do)s(es)i(not)f(con)m(tain)g(the)h
2833	(p)s(ole)f(explicitly)e(as)j(a)f(grid)324 4541 y(v)m(ertex,)43
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2837	b(.)470 4782 y(The)30 b(p)s(ole)f(also)f(creates)i(problems)f(for)g
2838	(the)g(searc)m(h)i(and)e(in)m(tersection)g(algorithms)324
2839	4902 y(describ)s(ed)38 b(ab)s(o)m(v)m(e.)59 b(F)-8 b(or)37
2840	b(example,)h(a)f(grid)g(cell)f(that)h(o)m(v)m(erlaps)h(the)g(p)s(ole)f
2841	(can)h(result)1894 5251 y(19)p eop
2842	%%Page: 20 22
2843	20 21 bop 324 548 a Fq(in)28 b(a)g(noncon)m(v)m(ex)j(cell)d(in)g
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2845	(test)324 668 y(describ)s(ed)42 b(ab)s(o)m(v)m(e)g(will)c(fail)h(in)i
2846	(this)f(case.)70 b(In)42 b(addition,)f(segmen)m(ts)i(near)e(the)h(p)s
2847	(ole)324 789 y(t)m(ypically)30 b(exhibit)h(large)g(c)m(hanges)i(in)e
2848	(longitude)g(ev)m(en)i(for)f(v)m(ery)h(short)f(segmen)m(ts.)44
2849	b(In)324 909 y(suc)m(h)31 b(a)f(case,)h(the)g(linear)d
2850	(parametrizations)g(used)j(ab)s(o)m(v)m(e)g(result)f(in)f(inaccuracies)
2851	h(for)324 1029 y(determining)h(the)i(correct)g(in)m(tersections.)470
2852	1150 y(T)-8 b(o)35 b(a)m(v)m(oid)g(these)i(problems,)e(a)g(co)s
2853	(ordinate)g(transformation)e(can)i(b)s(e)h(used)g(p)s(ole-)324
2854	1270 y(w)m(ard)e(of)g(a)f(giv)m(en)h(threshold)g(latitude)f(\(t)m
2855	(ypically)f(within)h(one)h(degree)h(of)e(the)h(p)s(ole\).)324
2856	1391 y(A)e(p)s(ossible)g(transformation)f(is)h(the)h(Lam)m(b)s(ert)f
2857	(equiv)-5 b(alen)m(t)32 b(azim)m(uthal)f(pro)5 b(jection)1365
2858	1667 y Fh(X)91 b Fq(=)83 b(2)17 b(sin)1898 1521 y Fe( )1973
2859	1600 y Fh(\031)p 1973 1644 59 4 v 1978 1736 a Fq(4)2064
2860	1667 y Fo(\000)2174 1600 y Fh(\022)p 2174 1644 49 4 v
2861	2174 1736 a Fq(2)2233 1521 y Fe(!)2315 1667 y Fq(cos)g
2862	Fh(\036)1376 1950 y(Y)104 b Fq(=)83 b(2)17 b(sin)1898
2863	1804 y Fe( )1973 1882 y Fh(\031)p 1973 1926 59 4 v 1978
2864	2018 a Fq(4)2064 1950 y Fo(\000)2174 1882 y Fh(\022)p
2865	2174 1926 49 4 v 2174 2018 a Fq(2)2233 1804 y Fe(!)2315
2866	1950 y Fq(sin)g Fh(\036)802 b Fq(\(3.17\))324 2226 y(for)35
2867	b(the)i(North)f(P)m(ole.)54 b(The)37 b(transformation)d(for)i(the)g
2868	(South)h(P)m(ole)f(is)f(similar.)51 b(This)324 2347 y(transformation)34
2869	b(is)h(only)h(used)h(to)f(compute)g(in)m(tersections;)i(line)d(in)m
2870	(tegrals)g(are)h(still)324 2467 y(computed)28 b(in)f
2871	(latitude-longitude)d(co)s(ordinates.)42 b(Because)29
2872	b(in)m(tersections)f(computed)324 2588 y(in)50 b(the)h(transformed)f
2873	(co)s(ordinates)g(can)h(b)s(e)f(di\013eren)m(t)h(from)e(those)j
2874	(computed)e(in)324 2708 y(latitude-longitude)23 b(co)s(ordinates,)k
2875	(line)f(segmen)m(ts)h(whic)m(h)g(cross)h(the)f(latitude)e(thresh-)324
2876	2828 y(old)33 b(m)m(ust)i(b)s(e)f(treated)h(carefully)-8
2877	b(.)48 b(T)-8 b(o)34 b(compute)h(the)f(in)m(tersections)h(consisten)m
2878	(tly)g(for)324 2949 y(suc)m(h)41 b(a)f(segmen)m(t,)j(in)m(tersections)e
2879	(with)f(the)g(threshold)h(latitude)d(are)j(detected)g(and)324
2880	3069 y(used)33 b(as)g(a)f(normal)f(grid)g(in)m(tersection)h(to)g(pro)m
2881	(vide)h(a)f(clean)g(break)i(b)s(et)m(w)m(een)g(the)f(t)m(w)m(o)324
2882	3189 y(co)s(ordinate)e(systems.)324 3522 y Fm(3.5)160
2883	b(Conclusion)324 3741 y Fq(The)27 b(implemen)m(tation)22
2884	b(in)j(the)i(SCRIP)g(co)s(de)f(follo)m(ws)e(closely)i(the)g
2885	(description)g(ab)s(o)m(v)m(e.)324 3862 y(The)34 b(user)g(should)f(b)s
2886	(e)h(able)f(to)g(follo)m(w)e(and)j(understand)g(the)g(pro)s(cess)g
2887	(based)h(on)e(this)324 3982 y(description.)1894 5251
2888	y(20)p eop
2889	%%Page: 21 23
2890	21 22 bop 324 1212 a Fn(Chapter)78 b(4)324 1627 y(Bilinear)e(Remapping)
2891	324 2080 y Fq(Standard)44 b(bilinear)d(in)m(terp)s(olation)g(sc)m
2892	(hemes)46 b(can)e(b)s(e)g(found)g(in)f(man)m(y)h(textb)s(o)s(oks.)324
2893	2200 y(Here)25 b(w)m(e)g(presen)m(t)g(a)f(more)f(general)h(sc)m(heme)h
2894	(whic)m(h)g(uses)g(a)f(lo)s(cal)e(bilinear)f(appro)m(xima-)324
2895	2320 y(tion)k(to)h(in)m(terp)s(olate)f(to)h(a)g(p)s(oin)m(t)f(in)h(a)g
2896	(quadrilateral)e(grid.)40 b(Consider)27 b(the)g(grid)e(p)s(oin)m(ts)324
2897	2441 y(sho)m(wn)34 b(in)d(Fig.)h(4.1)g(lab)s(elled)e(with)i
2898	(logically-rectangular)c(indices)33 b(\(e.g.)43 b(\()p
2899	Fh(i;)17 b(j)6 b Fq(\)\).)470 2561 y(Let)37 b(the)h(latitude-longitude)
2900	c(co)s(ordinates)i(of)h(p)s(oin)m(t)f(1)h(b)s(e)g(\()p
2901	Fh(\022)s Fq(\()p Fh(i;)17 b(j)6 b Fq(\))p Fh(;)17 b(\036)p
2902	Fq(\()p Fh(i;)g(j)6 b Fq(\)\),)37 b(the)324 2682 y(co)s(ordinates)g(of)
2903	g(p)s(oin)m(t)f(2)i(b)s(e)f(\()p Fh(\022)s Fq(\()p Fh(i)26
2904	b Fq(+)f(1)p Fh(;)17 b(j)6 b Fq(\))p Fh(;)17 b(\036)p
2905	Fq(\()p Fh(i)25 b Fq(+)g(1)p Fh(;)17 b(j)6 b Fq(\)\),)38
2906	b(etc.)59 b(No)m(w)38 b(let)f Fh(\013)h Fq(and)f Fh(\014)43
2907	b Fq(b)s(e)324 2802 y(con)m(tin)m(uous)36 b(lo)s(cal)d(co)s(ordinates)i
2908	(suc)m(h)i(that)e(the)h(co)s(ordinates)f(\()p Fh(\013)q(;)17
2909	b(\014)6 b Fq(\))34 b(of)h(p)s(oin)m(t)f(1)i(are)324
2910	2922 y(\(0)p Fh(;)17 b Fq(0\),)34 b(p)s(oin)m(t)f(2)h(are)h(\(1)p
2911	Fh(;)17 b Fq(0\),)34 b(p)s(oin)m(t)f(3)h(are)h(\(1)p
2912	Fh(;)17 b Fq(1\))33 b(and)i(p)s(oin)m(t)e(4)h(are)g(\(0)p
2913	Fh(;)17 b Fq(1\).)48 b(If)35 b(p)s(oin)m(t)e Fh(P)324
2914	3043 y Fq(lies)h(inside)g(the)i(cell)e(formed)h(b)m(y)h(the)f(four)g(p)
2915	s(oin)m(ts)g(ab)s(o)m(v)m(e,)i(the)e(function)g Fh(f)46
2916	b Fq(at)34 b(p)s(oin)m(t)324 3163 y Fh(P)46 b Fq(can)33
2917	b(b)s(e)f(appro)m(ximated)g(b)m(y)503 3383 y Fh(f)551
2918	3398 y Ff(P)693 3383 y Fq(=)83 b(\(1)22 b Fo(\000)h Fh(\013)q
2919	Fq(\)\(1)e Fo(\000)i Fh(\014)6 b Fq(\))p Fh(f)11 b Fq(\()p
2920	Fh(i;)17 b(j)6 b Fq(\))21 b(+)h Fh(\013)q Fq(\(1)f Fo(\000)i
2921	Fh(\014)6 b Fq(\))p Fh(f)11 b Fq(\()p Fh(i)22 b Fq(+)g(1)p
2922	Fh(;)17 b(j)6 b Fq(\))21 b(+)852 3528 y Fh(\013)q(\014)6
2923	b(f)11 b Fq(\()p Fh(i)21 b Fq(+)h(1)p Fh(;)17 b(j)28
2924	b Fq(+)22 b(1\))g(+)g(\(1)g Fo(\000)g Fh(\013)q Fq(\))p
2925	Fh(\014)6 b(f)11 b Fq(\()p Fh(i;)17 b(j)27 b Fq(+)22
2926	b(1\))874 b(\(4.1\))693 3674 y(=)83 b Fh(w)922 3689 y
2927	Fi(1)961 3674 y Fh(f)11 b Fq(\()p Fh(i;)17 b(j)6 b Fq(\))22
2928	b(+)g Fh(w)1409 3689 y Fi(2)1448 3674 y Fh(f)11 b Fq(\()p
2929	Fh(i)22 b Fq(+)g(1)p Fh(;)17 b(j)6 b Fq(\))22 b(+)g Fh(w)2065
2930	3689 y Fi(3)2104 3674 y Fh(f)11 b Fq(\()p Fh(i)22 b Fq(+)g(1)p
2931	Fh(;)17 b(j)27 b Fq(+)c(1\))e(+)h Fh(w)2889 3689 y Fi(4)2929
2932	3674 y Fh(f)11 b Fq(\()p Fh(i;)17 b(j)27 b Fq(+)22 b(1\))p
2933	Fh(:)324 3894 y Fq(The)37 b(remapping)f(w)m(eigh)m(ts)h(m)m(ust)g
2934	(therefore)g(b)s(e)g(computed)g(b)m(y)h(\014nding)e Fh(\013)h
2935	Fq(and)g Fh(\014)42 b Fq(at)324 4014 y(p)s(oin)m(t)31
2936	b Fh(P)14 b Fq(.)470 4134 y(The)38 b(latitude-longitude)33
2937	b(co)s(ordinates)j(\()p Fh(\022)s(;)17 b(\036)p Fq(\))37
2938	b(of)f(p)s(oin)m(t)g Fh(P)50 b Fq(are)36 b(kno)m(wn)i(and)f(can)324
2939	4255 y(also)31 b(b)s(e)i(appro)m(ximated)f(b)m(y)675
2940	4475 y Fh(\022)86 b Fq(=)d(\(1)22 b Fo(\000)h Fh(\013)q
2941	Fq(\)\(1)e Fo(\000)i Fh(\014)6 b Fq(\))p Fh(\022)1627
2942	4490 y Fi(1)1688 4475 y Fq(+)22 b Fh(\013)q Fq(\(1)g
2943	Fo(\000)g Fh(\014)6 b Fq(\))p Fh(\022)2201 4490 y Fi(2)2263
2944	4475 y Fq(+)22 b Fh(\013)q(\014)6 b(\022)2530 4490 y
2945	Fi(3)2591 4475 y Fq(+)22 b(\(1)g Fo(\000)h Fh(\013)q
2946	Fq(\))p Fh(\014)6 b(\022)3105 4490 y Fi(4)665 4620 y
2947	Fh(\036)83 b Fq(=)g(\(1)22 b Fo(\000)h Fh(\013)q Fq(\)\(1)e
2948	Fo(\000)i Fh(\014)6 b Fq(\))p Fh(\036)1640 4635 y Fi(1)1700
2949	4620 y Fq(+)22 b Fh(\013)q Fq(\(1)g Fo(\000)h Fh(\014)6
2950	b Fq(\))p Fh(\036)2227 4635 y Fi(2)2287 4620 y Fq(+)22
2951	b Fh(\013)q(\014)6 b(\036)2567 4635 y Fi(3)2628 4620
2952	y Fq(+)22 b(\(1)g Fo(\000)h Fh(\013)q Fq(\))p Fh(\014)6
2953	b(\036)3155 4635 y Fi(4)3193 4620 y Fh(:)141 b Fq(\(4.2\))324
2954	4840 y(Because)36 b(\(4.2\))e(is)g(nonlinear)f(in)g Fh(\013)j
2955	Fq(and)e Fh(\014)6 b Fq(,)35 b(w)m(e)g(m)m(ust)g(linearize)e(and)h
2956	(iterate)g(to)m(w)m(ard)1894 5251 y(21)p eop
2957	%%Page: 22 24
2958	22 23 bop 1063 1127 a Fq(Figure)31 b(4.1:)43 b(A)33 b(general)f
2959	(quadrilateral)e(grid.)656 4143 y Fc(\010)739 4102 y(\010)822
2960	4060 y(\010)905 4019 y(\010)988 3977 y(\010)1071 3936
2961	y(\010)1154 3894 y(\010)1237 3853 y(\010)1320 3811 y(\010)1403
2962	3770 y(\010)1486 3728 y(\010)1569 3687 y(\010)1652 3645
2963	y(\010)1735 3604 y(\010)1818 3562 y(\010)1901 3521 y(\010)1984
2964	3479 y(\010)2067 3438 y(\010)2150 3396 y(\010)2233 3355
2965	y(\010)2316 3313 y(\001)2358 3230 y(\001)2399 3147 y(\001)2441
2966	3064 y(\001)2482 2981 y(\001)2524 2898 y(\001)2565 2815
2967	y(\001)2607 2732 y(\001)2648 2649 y(\001)2690 2566 y(\001)2731
2968	2483 y(\001)2773 2400 y(\001)2814 2317 y(\001)2856 2234
2969	y(\001)2897 2151 y(\001)2939 2068 y(\001)2980 1985 y(\001)3022
2970	1902 y(\001)3064 1819 y(\001)3105 1736 y(\001)656 4143
2971	y(\001)697 4060 y(\001)739 3977 y(\001)780 3894 y(\001)822
2972	3811 y(\001)863 3728 y(\001)905 3645 y(\001)946 3562
2973	y(\001)988 3479 y(\001)1029 3396 y(\001)1071 3313 y(\001)1112
2974	3230 y(\001)1154 3147 y(\001)1196 3064 y(\001)1237 2981
2975	y(\001)1279 2898 y(\001)1320 2815 y(\001)1362 2732 y(\001)1403
2976	2649 y(\001)1445 2566 y(\001)1486 2483 y(\010)1569 2442
2977	y(\010)1652 2400 y(\010)1735 2359 y(\010)1818 2317 y(\010)1901
2978	2275 y(\010)1984 2234 y(\010)2067 2192 y(\010)2150 2151
2979	y(\010)2233 2109 y(\010)2316 2068 y(\010)2399 2026 y(\010)2482
2980	1985 y(\010)2565 1943 y(\010)2648 1902 y(\010)2731 1860
2981	y(\010)2814 1819 y(\010)2897 1777 y(\010)2980 1736 y(\010)3064
2982	1694 y(\010)656 4143 y Fa(s)2316 3313 y(s)1486 2483 y(s)3147
2983	1653 y(s)2067 2815 y(s)573 4310 y Fq(1)i(\()p Fh(i;)17
2984	b(j)6 b Fq(\))2399 3396 y(2)33 b(\()p Fh(i)22 b Fq(+)g(1)p
2985	Fh(;)17 b(j)6 b Fq(\))988 2483 y(\()p Fh(i;)17 b(j)28
2986	b Fq(+)22 b(1\))32 b(4)3230 1653 y(3)g(\()p Fh(i)22 b
2987	Fq(+)g(1)p Fh(;)17 b(j)28 b Fq(+)22 b(1\))1984 2815 y
2988	Fh(P)1894 5251 y Fq(22)p eop
2989	%%Page: 23 25
2990	23 24 bop 324 548 a Fq(a)32 b(solution.)42 b(Di\013eren)m(tiating)30
2991	b(\(4.2\))i(results)h(in)1523 684 y Fe(")1618 769 y Fh(\016)t(\022)1613
2992	890 y(\016)t(\036)1759 684 y Fe(#)1836 830 y Fq(=)27
2993	b Fh(A)2029 684 y Fe(")2119 769 y Fh(\016)t(\013)2120
2994	890 y(\016)t(\014)2270 684 y Fe(#)2335 830 y Fh(;)999
2995	b Fq(\(4.3\))324 1107 y(where)324 1364 y Fh(A)28 b Fq(=)528
2996	1218 y Fe(")655 1303 y Fq(\()p Fh(\022)738 1318 y Fi(2)800
2997	1303 y Fo(\000)22 b Fh(\022)944 1318 y Fi(1)984 1303
2998	y Fq(\))g(+)g(\()p Fh(\022)1225 1318 y Fi(1)1287 1303
2999	y Fo(\000)h Fh(\022)1432 1318 y Fi(4)1494 1303 y Fq(+)f
3000	Fh(\022)1637 1318 y Fi(3)1699 1303 y Fo(\000)h Fh(\022)1844
3001	1318 y Fi(2)1884 1303 y Fq(\))p Fh(\014)162 b Fq(\()p
3002	Fh(\022)2222 1318 y Fi(4)2284 1303 y Fo(\000)22 b Fh(\022)2428
3003	1318 y Fi(1)2468 1303 y Fq(\))g(+)g(\()p Fh(\022)2709
3004	1318 y Fi(1)2771 1303 y Fo(\000)h Fh(\022)2916 1318 y
3005	Fi(4)2978 1303 y Fq(+)f Fh(\022)3121 1318 y Fi(3)3183
3006	1303 y Fo(\000)h Fh(\022)3328 1318 y Fi(2)3368 1303 y
3007	Fq(\))p Fh(\013)618 1424 y Fq(\()p Fh(\036)714 1439 y
3008	Fi(2)775 1424 y Fo(\000)g Fh(\036)933 1439 y Fi(1)972
3009	1424 y Fq(\))f(+)g(\()p Fh(\036)1226 1439 y Fi(1)1287
3010	1424 y Fo(\000)h Fh(\036)1445 1439 y Fi(4)1506 1424 y
3011	Fq(+)f Fh(\036)1662 1439 y Fi(3)1724 1424 y Fo(\000)g
3012	Fh(\036)1881 1439 y Fi(2)1920 1424 y Fq(\))p Fh(\014)89
3013	b Fq(\()p Fh(\036)2198 1439 y Fi(4)2259 1424 y Fo(\000)23
3014	b Fh(\036)2417 1439 y Fi(1)2456 1424 y Fq(\))f(+)g(\()p
3015	Fh(\036)2710 1439 y Fi(1)2771 1424 y Fo(\000)h Fh(\036)2929
3016	1439 y Fi(4)2990 1424 y Fq(+)f Fh(\036)3146 1439 y Fi(3)3208
3017	1424 y Fo(\000)g Fh(\036)3365 1439 y Fi(2)3404 1424 y
3018	Fq(\))p Fh(\013)3547 1218 y Fe(#)3612 1364 y Fh(:)3361
3019	1547 y Fq(\(4.4\))324 1667 y(In)m(v)m(erting)33 b(this)f(system,)741
3020	1944 y Fh(\016)t(\013)c Fq(=)982 1795 y Fe(\014)982 1844
3021	y(\014)982 1894 y(\014)982 1944 y(\014)982 1994 y(\014)1056
3022	1883 y Fh(\016)t(\022)128 b Fq(\()p Fh(\022)1359 1898
3023	y Fi(4)1421 1883 y Fo(\000)22 b Fh(\022)1565 1898 y Fi(1)1605
3024	1883 y Fq(\))g(+)g(\()p Fh(\022)1846 1898 y Fi(1)1908
3025	1883 y Fo(\000)h Fh(\022)2053 1898 y Fi(4)2115 1883 y
3026	Fq(+)f Fh(\022)2258 1898 y Fi(3)2320 1883 y Fo(\000)g
3027	Fh(\022)2464 1898 y Fi(2)2504 1883 y Fq(\))p Fh(\013)1051
3028	2003 y(\016)t(\036)83 b Fq(\()p Fh(\036)1335 2018 y Fi(4)1396
3029	2003 y Fo(\000)23 b Fh(\036)1554 2018 y Fi(1)1593 2003
3030	y Fq(\))f(+)g(\()p Fh(\036)1847 2018 y Fi(1)1908 2003
3031	y Fo(\000)h Fh(\036)2066 2018 y Fi(4)2127 2003 y Fq(+)f
3032	Fh(\036)2283 2018 y Fi(3)2344 2003 y Fo(\000)h Fh(\036)2502
3033	2018 y Fi(2)2541 2003 y Fq(\))p Fh(\013)2683 1795 y Fe(\014)2683
3034	1844 y(\014)2683 1894 y(\014)2683 1944 y(\014)2683 1994
3035	y(\014)2733 1944 y Fo(\004)h Fq(det\()p Fh(A)p Fq(\))p
3036	Fh(;)217 b Fq(\(4.5\))324 2221 y(and)743 2379 y Fh(\016)t(\014)33
3037	b Fq(=)982 2229 y Fe(\014)982 2279 y(\014)982 2329 y(\014)982
3038	2379 y(\014)982 2428 y(\014)1088 2318 y Fq(\()p Fh(\022)1171
3039	2333 y Fi(2)1233 2318 y Fo(\000)23 b Fh(\022)1378 2333
3040	y Fi(1)1417 2318 y Fq(\))f(+)g(\()p Fh(\022)1658 2333
3041	y Fi(1)1720 2318 y Fo(\000)h Fh(\022)1865 2333 y Fi(4)1927
3042	2318 y Fq(+)f Fh(\022)2070 2333 y Fi(3)2132 2318 y Fo(\000)h
3043	Fh(\022)2277 2333 y Fi(2)2317 2318 y Fq(\))p Fh(\014)130
3044	b(\016)t(\022)1051 2438 y Fq(\()p Fh(\036)1147 2453 y
3045	Fi(2)1208 2438 y Fo(\000)23 b Fh(\036)1366 2453 y Fi(1)1405
3046	2438 y Fq(\))f(+)g(\()p Fh(\036)1659 2453 y Fi(1)1720
3047	2438 y Fo(\000)h Fh(\036)1878 2453 y Fi(4)1939 2438 y
3048	Fq(+)f Fh(\036)2095 2453 y Fi(3)2157 2438 y Fo(\000)g
3049	Fh(\036)2314 2453 y Fi(2)2354 2438 y Fq(\))p Fh(\014)88
3050	b(\016)t(\036)2681 2229 y Fe(\014)2681 2279 y(\014)2681
3051	2329 y(\014)2681 2379 y(\014)2681 2428 y(\014)2731 2379
3052	y Fo(\004)24 b Fq(det\()p Fh(A)p Fq(\))p Fh(:)219 b Fq(\(4.6\))324
3053	2615 y(Starting)34 b(with)i(an)f(initial)d(guess)37 b(for)e
3054	Fh(\013)i Fq(and)f Fh(\014)41 b Fq(\(sa)m(y)c Fh(\013)c
3055	Fq(=)g Fh(\014)39 b Fq(=)33 b(0\),)j(equations)g(\(4.5\))324
3056	2736 y(and)j(\(4.6\))f(can)h(b)s(e)h(iterated)e(un)m(til)g
3057	Fh(\016)t(\013)h Fq(and)g Fh(\016)t(\014)45 b Fq(are)39
3058	b(suitably)f(small.)60 b(The)40 b(w)m(eigh)m(ts)324 2856
3059	y(can)g(then)i(b)s(e)e(computed)h(from)e(\(4.1\).)66
3060	b(Note)41 b(that)f(for)g(simple)f(latitude-longitude)324
3061	2976 y(grids,)32 b(this)g(iteration)f(will)f(con)m(v)m(erge)k(in)e(the)
3062	h(\014rst)g(iteration.)470 3097 y(In)39 b(order)f(to)g(compute)g(the)h
3063	(w)m(eigh)m(ts)g(using)f(this)f(general)h(bilinear)e(iteration,)i(it)
3064	324 3217 y(m)m(ust)f(b)s(e)g(determined)g(in)f(whic)m(h)h(b)s(o)m(x)g
3065	(the)h(p)s(oin)m(t)e Fh(P)50 b Fq(resides.)57 b(F)-8
3066	b(or)36 b(this,)i(the)f(searc)m(h)324 3337 y(algorithms)27
3067	b(outlined)h(in)g(the)i(previous)g(c)m(hapter)h(are)e(used)i(with)e
3068	(the)h(exception)g(that)324 3458 y(instead)46 b(of)g(using)h(cell)e
3069	(corners,)51 b(the)c(relev)-5 b(an)m(t)46 b(b)s(o)m(x)h(is)f(formed)g
3070	(b)m(y)i(neigh)m(b)s(or)e(cell)324 3578 y(cen)m(ters)34
3071	b(as)f(sho)m(wn)h(in)e(Fig.)f(4.1.)1894 5251 y(23)p eop
3072	%%Page: 24 26
3073	24 25 bop 324 1212 a Fn(Chapter)78 b(5)324 1627 y(Bicubic)f(Remapping)
3074	324 2080 y Fq(The)42 b(bicubic)e(remapping)g(exactly)h(follo)m(ws)f
3075	(the)h(bilinear)e(remapping)g(except)k(that)324 2200
3076	y(four)29 b(w)m(eigh)m(ts)i(for)e(eac)m(h)i(corner)g(p)s(oin)m(t)e(are)
3077	g(required.)44 b(Th)m(us,)32 b(n)m(um)p 2824 2200 30
3078	4 v 35 w(wts)e(is)g(set)g(to)g(four)324 2320 y(for)i(this)g(option.)42
3079	b(The)34 b(bicubic)e(remapping)f(is)875 2540 y Fh(f)923
3080	2555 y Ff(P)1065 2540 y Fq(=)83 b(\(1)22 b Fo(\000)g
3081	Fh(\014)1493 2499 y Fi(2)1532 2540 y Fq(\(3)g Fo(\000)h
3082	Fq(2)p Fh(\014)6 b Fq(\)\)\(1)21 b Fo(\000)i Fh(\013)2198
3083	2499 y Fi(2)2237 2540 y Fq(\(3)f Fo(\000)g Fq(2)p Fh(\013)q
3084	Fq(\)\))p Fh(f)11 b Fq(\()p Fh(i;)17 b(j)6 b Fq(\))21
3085	b(+)1224 2686 y(\(1)h Fo(\000)g Fh(\014)1493 2645 y Fi(2)1532
3086	2686 y Fq(\(3)g Fo(\000)h Fq(2)p Fh(\014)6 b Fq(\)\))p
3087	Fh(\013)1990 2645 y Fi(2)2028 2686 y Fq(\(3)22 b Fo(\000)h
3088	Fq(2)p Fh(\013)q Fq(\))p Fh(f)11 b Fq(\()p Fh(i)21 b
3089	Fq(+)h(1)p Fh(;)17 b(j)6 b Fq(\))22 b(+)1224 2831 y Fh(\014)1285
3090	2790 y Fi(2)1324 2831 y Fq(\(3)g Fo(\000)g Fq(2)p Fh(\014)6
3091	b Fq(\))p Fh(\013)1743 2790 y Fi(2)1782 2831 y Fq(\(3)22
3092	b Fo(\000)g Fq(2)p Fh(\013)q Fq(\))p Fh(f)11 b Fq(\()p
3093	Fh(i)22 b Fq(+)g(1)p Fh(;)17 b(j)27 b Fq(+)22 b(1\))g(+)1224
3094	2976 y Fh(\014)1285 2935 y Fi(2)1324 2976 y Fq(\(3)g
3095	Fo(\000)g Fq(2)p Fh(\014)6 b Fq(\)\(1)22 b Fo(\000)g
3096	Fh(\013)1951 2935 y Fi(2)1990 2976 y Fq(\(3)g Fo(\000)h
3097	Fq(2)p Fh(\013)q Fq(\)\))p Fh(f)11 b Fq(\()p Fh(i;)17
3098	b(j)27 b Fq(+)22 b(1\))g(+)1224 3171 y(\(1)g Fo(\000)g
3099	Fh(\014)1493 3130 y Fi(2)1532 3171 y Fq(\(3)g Fo(\000)h
3100	Fq(2)p Fh(\014)6 b Fq(\)\))p Fh(\013)q Fq(\()p Fh(\013)22
3101	b Fo(\000)g Fq(1\))2298 3130 y Fi(2)2347 3104 y Fh(@)5
3102	b(f)p 2347 3148 116 4 v 2360 3239 a(@)g(i)2473 3171 y
3103	Fq(\()p Fh(i;)17 b(j)6 b Fq(\))22 b(+)1224 3409 y(\(1)g
3104	Fo(\000)g Fh(\014)1493 3368 y Fi(2)1532 3409 y Fq(\(3)g
3105	Fo(\000)h Fq(2)p Fh(\014)6 b Fq(\)\))p Fh(\013)1990 3368
3106	y Fi(2)2028 3409 y Fq(\()p Fh(\013)23 b Fo(\000)g Fq(1\))2348
3107	3342 y Fh(@)5 b(f)p 2348 3386 V 2361 3478 a(@)g(i)2473
3108	3409 y Fq(\()p Fh(i)22 b Fq(+)g(1)p Fh(;)17 b(j)6 b Fq(\))22
3109	b(+)1224 3647 y Fh(\014)1285 3606 y Fi(2)1324 3647 y
3110	Fq(\(3)g Fo(\000)g Fq(2)p Fh(\014)6 b Fq(\))p Fh(\013)1743
3111	3606 y Fi(2)1782 3647 y Fq(\()p Fh(\013)23 b Fo(\000)f
3112	Fq(1\))2101 3580 y Fh(@)5 b(f)p 2101 3624 V 2114 3716
3113	a(@)g(i)2226 3647 y Fq(\()p Fh(i)23 b Fq(+)f(1)p Fh(;)17
3114	b(j)27 b Fq(+)22 b(1\))g(+)1224 3885 y Fh(\014)1285 3844
3115	y Fi(2)1324 3885 y Fq(\(3)g Fo(\000)g Fq(2)p Fh(\014)6
3116	b Fq(\))p Fh(\013)q Fq(\()p Fh(\013)22 b Fo(\000)h Fq(1\))2052
3117	3844 y Fi(2)2101 3818 y Fh(@)5 b(f)p 2101 3862 V 2114
3118	3954 a(@)g(i)2226 3885 y Fq(\()p Fh(i;)17 b(j)29 b Fq(+)22
3119	b(1\))f(+)1224 4124 y Fh(\014)6 b Fq(\()p Fh(\014)27
3120	b Fo(\000)c Fq(1\))1592 4082 y Fi(2)1631 4124 y Fq(\(1)f
3121	Fo(\000)g Fh(\013)1902 4082 y Fi(2)1942 4124 y Fq(\(3)f
3122	Fo(\000)i Fq(2)p Fh(\013)q Fq(\)\))2348 4056 y Fh(@)5
3123	b(f)p 2348 4100 V 2354 4192 a(@)g(j)2473 4124 y Fq(\()p
3124	Fh(i;)17 b(j)6 b Fq(\))22 b(+)1224 4381 y Fh(\014)6 b
3125	Fq(\()p Fh(\014)27 b Fo(\000)c Fq(1\))1592 4340 y Fi(2)1631
3126	4381 y Fh(\013)1694 4340 y Fi(2)1733 4381 y Fq(\(3)f
3127	Fo(\000)h Fq(2)p Fh(\013)q Fq(\))2102 4314 y Fh(@)5 b(f)p
3128	2102 4358 V 2108 4449 a(@)g(j)2226 4381 y Fq(\()p Fh(i)23
3129	b Fq(+)f(1)p Fh(;)17 b(j)6 b Fq(\))21 b(+)1224 4639 y
3130	Fh(\014)1285 4597 y Fi(2)1324 4639 y Fq(\()p Fh(\014)28
3131	b Fo(\000)22 b Fq(1\))p Fh(\013)1694 4597 y Fi(2)1733
3132	4639 y Fq(\(3)g Fo(\000)h Fq(2)p Fh(\013)q Fq(\))2102
3133	4571 y Fh(@)5 b(f)p 2102 4615 V 2108 4707 a(@)g(j)2226
3134	4639 y Fq(\()p Fh(i)23 b Fq(+)f(1)p Fh(;)17 b(j)27 b
3135	Fq(+)22 b(1\))g(+)1224 4896 y Fh(\014)1285 4855 y Fi(2)1324
3136	4896 y Fq(\()p Fh(\014)28 b Fo(\000)22 b Fq(1\)\(1)g
3137	Fo(\000)g Fh(\013)1902 4855 y Fi(2)1942 4896 y Fq(\(3)f
3138	Fo(\000)i Fq(2)p Fh(\013)q Fq(\)\))2348 4829 y Fh(@)5
3139	b(f)p 2348 4873 V 2354 4964 a(@)g(j)2473 4896 y Fq(\()p
3140	Fh(i;)17 b(j)28 b Fq(+)22 b(1\))g(+)1894 5251 y(24)p
3141	eop
3142	%%Page: 25 27
3143	25 26 bop 1224 595 a Fh(\013)q Fq(\()p Fh(\013)22 b Fo(\000)h
3144	Fq(1\))1596 554 y Fi(2)1635 595 y Fh(\014)6 b Fq(\()p
3145	Fh(\014)27 b Fo(\000)c Fq(1\))2003 554 y Fi(2)2071 527
3146	y Fh(@)2127 491 y Fi(2)2167 527 y Fh(f)p 2052 571 194
3147	4 v 2052 663 a(@)5 b(i@)g(j)2255 595 y Fq(\()p Fh(i;)17
3148	b(j)6 b Fq(\))22 b(+)1224 862 y Fh(\013)1287 821 y Fi(2)1326
3149	862 y Fq(\()p Fh(\013)h Fo(\000)f Fq(1\))p Fh(\014)6
3150	b Fq(\()p Fh(\014)27 b Fo(\000)c Fq(1\))2003 821 y Fi(2)2071
3151	795 y Fh(@)2127 758 y Fi(2)2167 795 y Fh(f)p 2052 839
3152	V 2052 930 a(@)5 b(i@)g(j)2255 862 y Fq(\()p Fh(i)23
3153	b Fq(+)f(1)p Fh(;)17 b(j)6 b Fq(\))21 b(+)1224 1129 y
3154	Fh(\013)1287 1088 y Fi(2)1326 1129 y Fq(\()p Fh(\013)i
3155	Fo(\000)f Fq(1\))p Fh(\014)1696 1088 y Fi(2)1735 1129
3156	y Fq(\()p Fh(\014)28 b Fo(\000)22 b Fq(1\))2071 1062
3157	y Fh(@)2127 1026 y Fi(2)2167 1062 y Fh(f)p 2052 1106
3158	V 2052 1198 a(@)5 b(i@)g(j)2255 1129 y Fq(\()p Fh(i)23
3159	b Fq(+)f(1)p Fh(;)17 b(j)27 b Fq(+)22 b(1\))g(+)1224
3160	1396 y Fh(\013)q Fq(\()p Fh(\013)g Fo(\000)h Fq(1\))1596
3161	1355 y Fi(2)1635 1396 y Fh(\014)1696 1355 y Fi(2)1735
3162	1396 y Fq(\()p Fh(\014)28 b Fo(\000)22 b Fq(1\))2071
3163	1329 y Fh(@)2127 1293 y Fi(2)2167 1329 y Fh(f)p 2052
3164	1373 V 2052 1465 a(@)5 b(i@)g(j)2255 1396 y Fq(\()p Fh(i;)17
3165	b(j)28 b Fq(+)22 b(1\))738 b(\(5.1\))324 1661 y(where)30
3166	b Fh(\013)f Fq(and)g Fh(\014)34 b Fq(are)28 b(iden)m(tical)f(to)i
3167	(those)g(found)f(in)g(the)h(bilinear)e(case)i(and)g(are)f(found)324
3168	1782 y(using)k(an)h(iden)m(tical)e(algorithm.)42 b(Note)33
3169	b(that)f(unlik)m(e)h(the)g(conserv)-5 b(ativ)m(e)34 b(remappings,)324
3170	1902 y(the)h(gradien)m(ts)f(here)i(are)e(gradien)m(ts)h(with)f(resp)s
3171	(ect)i(to)e(the)h Fg(lo)-5 b(gic)g(al)33 b Fq(v)-5 b(ariable)33
3172	b(and)i(not)324 2022 y(latitude)28 b(or)h(longitude.)42
3173	b(Lastly)-8 b(,)29 b(the)i(four)e(w)m(eigh)m(ts)i(corresp)s(onding)e
3174	(to)h(eac)m(h)g(address)324 2143 y(pair)39 b(corresp)s(ond)h(to)g(the)g
3175	(w)m(eigh)m(t)g(m)m(ultiplying)d(the)j(\014eld)f(v)-5
3176	b(alue)40 b(at)f(the)h(p)s(oin)m(t,)h(the)324 2263 y(w)m(eigh)m(t)29
3177	b(m)m(ultiplying)c(the)k(gradien)m(t)f(with)h(resp)s(ect)h(to)e
3178	Fh(i)p Fq(,)i(the)f(w)m(eigh)m(t)g(m)m(ultiplying)c(the)324
3179	2384 y(gradien)m(t)33 b(with)h(resp)s(ect)h(to)f Fh(j)6
3180	b Fq(,)34 b(and)g(the)h(w)m(eigh)m(t)f(m)m(ultiplying)d(the)j(cross)h
3181	(gradien)m(t)e(in)324 2504 y(that)f(order.)1894 5251
3182	y(25)p eop
3183	%%Page: 26 28
3184	26 27 bop 324 1212 a Fn(Chapter)78 b(6)324 1627 y(Distance-w)-6
3185	b(eigh)g(ted)77 b(Av)-6 b(erage)324 1876 y(Remapping)324
3186	2329 y Fq(This)42 b(sc)m(heme)h(for)e(remapping)g(is)g(probably)h(the)g
3187	(simplest)f(in)g(this)h(pac)m(k)-5 b(age.)72 b(The)324
3188	2449 y(co)s(de)30 b(simply)f(searc)m(hes)j(for)d(the)i(n)m(um)p
3189	1736 2449 30 4 v 35 w(neigh)m(b)s(ors)f(nearest)h(neigh)m(b)s(ors)f
3190	(and)g(computes)324 2570 y(the)j(w)m(eigh)m(ts)g(using)1297
3191	2739 y Fh(w)d Fq(=)1839 2672 y(1)p Fh(=)p Fq(\()p Fh(d)21
3192	b Fq(+)h Fh(\017)p Fq(\))p 1510 2716 1042 4 v 1510 2746
3193	a Fe(P)1598 2772 y Fi(n)n(um)p 1740 2772 30 4 v 34 w(neigh)n(b)r(ors)
3194	1598 2837 y Ff(n)2067 2812 y Fq([1)p Fh(=)p Fq(\()p Fh(d)2281
3195	2827 y Ff(n)2349 2812 y Fq(+)g Fh(\017)p Fq(\)])2562
3196	2739 y Fh(;)772 b Fq(\(6.1\))324 2969 y(where)29 b Fh(\017)f
3197	Fq(is)f(a)h(small)d(n)m(um)m(b)s(er)j(to)f(prev)m(en)m(t)j(dividing)c
3198	(b)m(y)j(zero,)g(the)f(sum)g(is)f(for)g(normal-)324 3089
3199	y(ization)37 b(and)j Fh(d)f Fq(is)g(the)g(distance)h(from)e(the)i
3200	(destination)e(grid)g(p)s(oin)m(t)h(to)g(the)h(source)324
3201	3209 y(grid)31 b(p)s(oin)m(t.)43 b(The)33 b(distance)g(is)f(the)h
3202	(angular)f(distance)452 3429 y Fh(d)27 b Fq(=)h(cos)764
3203	3388 y Fj(\000)p Fi(1)875 3429 y Fq(\(cos)17 b Fh(\022)1105
3204	3444 y Ff(d)1163 3429 y Fq(cos)g Fh(\022)1355 3444 y
3205	Ff(s)1392 3429 y Fq(\(cos)g Fh(\036)1635 3444 y Ff(d)1692
3206	3429 y Fq(cos)g Fh(\036)1897 3444 y Ff(s)1956 3429 y
3207	Fq(+)22 b(sin)16 b Fh(\036)2248 3444 y Ff(d)2305 3429
3208	y Fq(sin)h Fh(\036)2500 3444 y Ff(s)2536 3429 y Fq(\))22
3209	b(+)g(sin)17 b Fh(\022)2876 3444 y Ff(d)2933 3429 y Fq(sin)f
3210	Fh(\022)3114 3444 y Ff(s)3152 3429 y Fq(\))g Fh(;)128
3211	b Fq(\(6.2\))324 3649 y(where)33 b Fh(\022)j Fq(is)c(latitude,)f
3212	Fh(\036)h Fq(is)f(longitude)g(and)i(the)f(subscripts)i
3213	Fh(d;)17 b(s)32 b Fq(denote)h(destination)324 3770 y(and)f(source)i
3214	(grids,)e(resp)s(ectiv)m(ely)-8 b(.)470 3890 y(When)41
3215	b(\014nding)e(nearest)i(neigh)m(b)s(ors,)g(the)f(distance)g(is)f(not)h
3216	(computed)g(b)s(et)m(w)m(een)324 4011 y(the)30 b(destination)f(grid)g
3217	(p)s(oin)m(t)g(and)h(ev)m(ery)h(source)g(grid)e(p)s(oin)m(t.)42
3218	b(Instead,)32 b(the)e(searc)m(h)h(is)324 4131 y(narro)m(w)m(ed)i(b)m(y)
3219	g(sorting)e(the)i(t)m(w)m(o)f(grids)g(in)m(to)f(latitude)g(bins.)43
3220	b(Only)32 b(those)h(source)g(grid)324 4251 y(cells)28
3221	b(lying)g(in)h(the)h(same)f(latitude)f(bin)g(as)i(the)g(destination)e
3222	(grid)g(cell)g(are)i(c)m(hec)m(k)m(ed)i(to)324 4372 y(\014nd)h(the)g
3223	(nearest)g(neigh)m(b)s(ors.)1894 5251 y(26)p eop
3224	%%Page: 27 29
3225	27 28 bop 324 1212 a Fn(Chapter)78 b(7)324 1627 y(Bugs)324
3226	2080 y Fq(A)43 b(\014le)f(called)f(`bugs')j(is)e(included)g(in)g(the)i
3227	(distribution)c(whic)m(h)k(lists)d(curren)m(t)j(out-)324
3228	2200 y(standing)35 b(bugs)h(as)f(w)m(ell)g(as)h(a)f(v)m(ersion)h
3229	(history)-8 b(.)52 b(An)m(y)36 b(further)g(bugs,)h(commen)m(ts,)f(or)
3230	324 2320 y(suggestions)d(should)f(b)s(e)h(sen)m(t)h(to)e(me)g(at)g(p)m
3231	(wjones@lanl.go)m(v.)470 2441 y(The)d(co)s(de)g(do)s(es)f(not)h(ha)m(v)
3232	m(e)g(v)m(ery)h(useful)e(error)g(messages)h(to)f(help)g(diagnose)g
3233	(prob-)324 2561 y(lems)k(so)g(feel)g(free)h(to)g(p)s(ester)g(me)f(with)
3234	g(an)m(y)i(problems)e(y)m(ou)h(encoun)m(ter.)470 2682
3235	y(The)25 b(pac)m(k)-5 b(age)25 b(has)g(also)f(not)g(b)s(een)h(extensiv)
3236	m(ely)h(tested)g(on)e(a)g(v)-5 b(ariet)m(y)25 b(of)f(mac)m(hines.)324
3237	2802 y(It)33 b(w)m(orks)i(\014ne)g(on)e(SGI)h(mac)m(hines)f(and)h(IBM)g
3238	(mac)m(hines,)g(but)g(has)g(not)f(b)s(een)i(run)f(on)324
3239	2922 y(other)41 b(mac)m(hines.)68 b(It)41 b(is)f(prett)m(y)i(v)-5
3240	b(anilla)38 b(F)-8 b(ortran,)42 b(so)f(should)g(b)s(e)g(ok)g(on)g(mac)m
3241	(hines)324 3043 y(with)32 b(standard-complian)m(t)f(F90)g(compilers.)
3242	1894 5251 y(27)p eop
3243	%%Trailer
3244	end
3245	userdict /end-hook known{end-hook}if
3246	%%EOF

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