Estuarine Bayesian Single-station Estimation method for ecosystem metabolism
Source:R/ebase.R
ebase.RdEstuarine Bayesian Single-station Estimation method for ecosystem metabolism
Arguments
- dat
input data frame
- Z
numeric as single value for water column depth (m) or vector equal in length to number of rows in
dat- interval
timestep interval in seconds
- ndays
numeric for number of days in
datfor optimizing the metabolic equation, see details- aprior
numeric vector of length two indicating the mean and standard deviation for the prior distribution of the a parameter, see details
- rprior
numeric vector of length two indicating the mean and standard deviation for the prior distribution of the R parameter, see details
- bprior
numeric vector of length two indicating the mean and standard deviation for the prior distribution of the b parameter, see details
- bmax
numeric value for the upper limit on the prior distribution for
bprior, set as twice the default value of the mean- nogas
logical indicating if gas exchange is not included in the metabolic model, see details
- doave
logical indicating if the average dissolved oxygen concentration is used as the starting value for the estimation (default), otherwise the first observation will be used if
FALSE, see details- maxinterp
numeric value for minimum number of continuous observations that must not be interpolated within a group defined by
ndaysto assign asNAin output, see details- n.iter
number of MCMC iterations, passed to
jags- update.chains
logical to run
metab_updateif chains do not converge- n.burnin
number of MCMC chains to delete, passed to
jags- n.chains
number of MCMC chains to run, passed to
jags- n.thin
number of nth iterations to save for each chain, passed to
jags- model_file
NULLto use the model file included with the package or a path to a model text file can be used
Value
A data frame with metabolic estimates for areal gross production (P, O2 mmol m-2 d-1), respiration (R, O2 mmol m-2 d-1), and gas exchange (D, O2 mmol m-2 d-1, positive values as ingassing, negative values as outgassing). NEM (net ecosystem metabolism, O2 mmol m-2 d-1) is also returned as P - R. Additional parameters estimated by the model that are returned include a and b. The a parameter is a constant that represents the primary production per quantum of light with units of (mmol m-2 d-1)/(W m-2) and is used to estimate gross production (Grace et al., 2015). The b parameter is a constant used to estimate gas exchange in (cm hr-1)/(m2 s-2) (provided as 0.251 in eqn. 4 in Wanninkhof 2014). Observed dissolved oxygen (DO_obs, mmol m-3), modeled dissolved oxygen (DO_mod, mmol m-3), and delta dissolved oxygen of the modeled results (dDO, mmol m-3 d-1) are also returned. Note that delta dissolved oxygen is a daily rate.
95% credible intervals for a, b, and R are also returned in the corresponding columns alo, ahi, blo, bhi, Rlo, and Rhi, for the 2.5th and 97.5th percentile estimates for each parameter, respectively. These values indicate the interval within which there is a 95% probability that the true parameter is in this range. Note that all values for these parameters are repeated across rows, although only one estimate for each is returned based on the number of days defined by ndays.
Model fit can also be assessed using the converge and rsq columns. The values in these columns apply to each group in the grp column as specified with the ndays argument. The converge column indicates "Check convergence" or "Fine" if the JAGS estimate converged at that iteration (repeated across rows for the group). The n.chains argument can be increased if convergence is not achieved. Similarly, the rsq column shows the r-squared values of the linear fit between the modeled and observed dissolved oxygen (repeated across rows for the group). These values can also be viewed with fit_plot.
The nogas argument can be set to TRUE to exclude gas exchange from the metabolic estimates. This will force the prior distribution for b as mean 0 and standard deviation approximately 0.
Details
Required input data are time series for dissolved oxygen (mg L-1), water temperature (C), salinity (psu), total PAR (W m-2), and wind speed (m s-1). See the exdat example data file for a representation of the required data. Data are typically from continuously monitored water quality and weather parameters are hourly of sub-hourly time steps. Oxygen concentrations are converted to mmol/m3 prior to metabolic estimation. Water column depth is also required. This can be supplied as a single value or a vector of length equal to the number of rows in dat.
The metabolic estimates are based on a mass balance equation in Grace et al. 2015 with the gas exchange estimate from Wanninkhof 2004. It is similar to that provided by the BASEmetab R package at https://github.com/dgiling/BASEmetab, with modifications to estimate different parameters. The equation optimized in the JAGS model is:
$$ Z\frac{dC_d}{dt} = aPAR - R + bU_{10}^2\left(\frac{Sc}{600} \right)^{-0.5} \left(C_{Sat} - C_d \right )$$
More simply:
$$ Z\frac{dC_d}{dt} = P - R + D$$
Net ecosystem metabolism (NEM) is then estimated as:
$$NEM = P - R$$
Gross production is provided by aPAR, respiration is provided by R, and gas exchange is provided by the remainder. The likelihood of the parameters a, R, and b given the observed data are estimated from the JAGS model using prior distributions shown in the model file. At each time step, the change in oxygen concentration between time steps is calculated from the equation using model inputs and parameter guesses, and then a finite difference approximation is used to estimate modeled oxygen concentration. The first modeled value starts at the mean oxygen concentration for all measurements in the optimization period. The estimated concentration at each time step is also returned for comparison to observed as one measure of model performance.
The prior distributions for the a, R, and b parameters are defined in the model file included with the package as normal distributions with mean and standard deviations provided by the aprior, rprior, and bprior arguments. The default values were chosen based on approximate values from national syntheses of metabolic estimates. An additional constraint is that all the prior distributions are truncated to be positive values as required by the core metabolism equation above. The upper limit for b is set as two times 0.251, as given in eqn. 4 in Wanninkhof 2014. Units for each parameter are (mmol m-2 d-1)/(W m-2) for a, mmol m-2 d-1 for R, and (cm hr-1)/(m2 s-2) for b.
The ndays argument defines the model optimization period as the number of days that are used for optimizing the above mass balance equation. By default, this is done each day, i.e., ndays= 1 such that a loop is used that applies the model equation to observations within each day, evaluated iteratively from the first observation in a day to the last. Individual parameter estimates for a, R, and b are then returned for each day. However, more days can be used to estimate the unknown parameters, such that the loop can be evaluated for every ndays specified by the argument. The ndays argument will separate the input data into groups of consecutive days, where each group has a total number of days equal to ndays. The final block may not include the complete number of days specified by ndays if the number of unique dates in the input data includes a remainder when divided by ndays, e.g., if seven days are in the input data and ndays = 5, there will be two groups where the first has five days and the second has two days. The output data from ebase includes a column that specifies the grouping that was used based on ndays.
Missing values in the input data are also interpolated prior to estimating metabolism. It is the responsibility of the user to verify that these interpolated values are not wildly inaccurate. Missing values are linearly interpolated between non-missing values at the time step specified by the value in interval. This works well for small gaps, but can easily create inaccurate values at gaps larger than a few hours. The interp_plot function can be used to visually assess the interpolated values. Records at the start or end of the input time series that do not include a full day are also removed. A warning is returned to the console if gaps are found or dangling records are found.
The maxinterp argument specifies a minimum number of observations that must not be interpolated within groups defined by ndays that are assigned NA in the output (except Date and DateTimeStamp). Groups with continuous rows of interpolated values with length longer than this argument are assigned NA. The default value is half a day, i.e., 43200 seconds divided by the value in interval.
The doave argument can be used to define which dissolved oxygen value is used as the starting point in the Bayesian estimation for the optimization period. The default setting (doave = TRUE) will use the average of all the dissolved oxygen values in the optimization period defined by ndays. For example, the average of all dissolved oxygen values in each 24 hour period will be used if doave = TRUE and ndays = 1. The first dissolved oxygen observation of the time series in the optimization period will be used as the starting point if doave = F. In this case, the simulated dissolved oxygen time series will always start at the first observed dissolved oxygen value for each optimization period.
References
Grace, M.R., Giling, D.P., Hladyz, S., Caron, V., Thompson, R.M., Nally, R.M., 2015. Fast processing of diel oxygen curves: Estimating stream metabolism with BASE (BAyesian Single-station Estimation). Limnology and Oceanography: Methods 13, e10011. https://doi.org/10.1002/lom3.10011
Wanninkhof, R., 2014. Relationship between wind speed and gas exchange over the ocean revisited. Limnology and Oceanography: Methods 12, 351–362. https://doi.org/10.4319/lom.2014.12.351
Examples
# get one day of data
dat <- exdat[as.Date(exdat$DateTimeStamp, tz = 'America/Jamaica') == as.Date('2012-06-01'), ]
# run ebase, use more chains and iterations for a better fit, update.chains as T
ebase(dat, interval = 900, Z = 1.85, n.chains = 2, n.iter = 50,
update.chains = FALSE)
#> Warning: executing %dopar% sequentially: no parallel backend registered
#> Loading required package: rjags
#> Loading required package: coda
#> Linked to JAGS 4.3.0
#> Loaded modules: basemod,bugs
#>
#> Attaching package: ‘R2jags’
#> The following object is masked from ‘package:coda’:
#>
#> traceplot
#>
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#>
#> filter, lag
#> The following objects are masked from ‘package:base’:
#>
#> intersect, setdiff, setequal, union
#> DateTimeStamp Date grp Z DO_obs DO_mod DO_modlo DO_modhi
#> 1 2012-06-01 00:00:00 2012-06-01 1 1.85 140.625 166.1132 166.1126 166.1138
#> 2 2012-06-01 00:15:00 2012-06-01 1 1.85 159.375 165.3935 165.3220 165.5432
#> 3 2012-06-01 00:30:00 2012-06-01 1 1.85 150.000 164.7099 164.5634 165.0194
#> 4 2012-06-01 00:45:00 2012-06-01 1 1.85 150.000 164.0037 163.7845 164.4663
#> 5 2012-06-01 01:00:00 2012-06-01 1 1.85 150.000 163.2883 162.9972 163.9008
#> 6 2012-06-01 01:15:00 2012-06-01 1 1.85 156.250 162.5434 162.1829 163.2974
#> 7 2012-06-01 01:30:00 2012-06-01 1 1.85 168.750 161.8078 161.3773 162.7054
#> 8 2012-06-01 01:45:00 2012-06-01 1 1.85 168.750 161.0710 160.5707 162.1115
#> 9 2012-06-01 02:00:00 2012-06-01 1 1.85 165.625 160.3363 159.7663 161.5200
#> 10 2012-06-01 02:15:00 2012-06-01 1 1.85 165.625 159.6247 158.9835 160.9572
#> 11 2012-06-01 02:30:00 2012-06-01 1 1.85 150.000 158.8924 158.1816 160.3680
#> 12 2012-06-01 02:45:00 2012-06-01 1 1.85 159.375 158.2528 157.4662 159.8946
#> 13 2012-06-01 03:00:00 2012-06-01 1 1.85 131.250 157.5133 156.6577 159.2957
#> 14 2012-06-01 03:15:00 2012-06-01 1 1.85 118.750 156.7306 155.8091 158.6429
#> 15 2012-06-01 03:30:00 2012-06-01 1 1.85 121.875 155.9822 154.9926 158.0324
#> 16 2012-06-01 03:45:00 2012-06-01 1 1.85 115.625 155.2355 154.1778 157.4239
#> 17 2012-06-01 04:00:00 2012-06-01 1 1.85 118.750 154.5368 153.4081 156.8745
#> 18 2012-06-01 04:15:00 2012-06-01 1 1.85 131.250 153.7835 152.5872 156.2575
#> 19 2012-06-01 04:30:00 2012-06-01 1 1.85 156.250 153.1179 151.8489 155.7483
#> 20 2012-06-01 04:45:00 2012-06-01 1 1.85 162.500 152.4391 151.0983 155.2225
#> 21 2012-06-01 05:00:00 2012-06-01 1 1.85 134.375 151.7478 150.3362 154.6809
#> 22 2012-06-01 05:15:00 2012-06-01 1 1.85 150.000 151.0578 149.5754 154.1406
#> 23 2012-06-01 05:30:00 2012-06-01 1 1.85 150.000 150.6448 149.0761 153.9393
#> 24 2012-06-01 05:45:00 2012-06-01 1 1.85 146.875 150.1248 148.4763 153.6060
#> 25 2012-06-01 06:00:00 2012-06-01 1 1.85 150.000 149.4518 147.7335 153.0811
#> 26 2012-06-01 06:15:00 2012-06-01 1 1.85 150.000 148.7725 146.9885 152.5382
#> 27 2012-06-01 06:30:00 2012-06-01 1 1.85 137.500 148.1075 146.2624 151.9978
#> 28 2012-06-01 06:45:00 2012-06-01 1 1.85 140.625 147.4426 145.5408 151.4447
#> 29 2012-06-01 07:00:00 2012-06-01 1 1.85 150.000 146.8060 144.8515 150.9108
#> 30 2012-06-01 07:15:00 2012-06-01 1 1.85 153.125 146.2360 144.2331 150.4359
#> 31 2012-06-01 07:30:00 2012-06-01 1 1.85 159.375 145.9500 143.9422 150.1416
#> 32 2012-06-01 07:45:00 2012-06-01 1 1.85 168.750 146.1790 144.1881 150.3368
#> 33 2012-06-01 08:00:00 2012-06-01 1 1.85 168.750 146.6067 144.6472 150.7040
#> 34 2012-06-01 08:15:00 2012-06-01 1 1.85 168.750 146.5962 144.5981 150.8006
#> 35 2012-06-01 08:30:00 2012-06-01 1 1.85 162.500 147.0068 145.0675 151.0649
#> 36 2012-06-01 08:45:00 2012-06-01 1 1.85 165.625 147.5822 145.7171 151.4479
#> 37 2012-06-01 09:00:00 2012-06-01 1 1.85 168.750 148.4423 146.6538 152.1143
#> 38 2012-06-01 09:15:00 2012-06-01 1 1.85 171.875 149.4842 147.7818 152.9424
#> 39 2012-06-01 09:30:00 2012-06-01 1 1.85 171.875 151.3224 149.5144 154.7564
#> 40 2012-06-01 09:45:00 2012-06-01 1 1.85 168.750 153.3084 151.0879 156.7723
#> 41 2012-06-01 10:00:00 2012-06-01 1 1.85 168.750 153.5643 151.0514 157.3020
#> 42 2012-06-01 10:15:00 2012-06-01 1 1.85 175.000 153.7756 151.1353 157.5758
#> 43 2012-06-01 10:30:00 2012-06-01 1 1.85 178.125 154.1028 151.4211 157.8240
#> 44 2012-06-01 10:45:00 2012-06-01 1 1.85 178.125 155.4089 152.7609 158.7262
#> 45 2012-06-01 11:00:00 2012-06-01 1 1.85 178.125 156.6951 154.1425 159.5301
#> 46 2012-06-01 11:15:00 2012-06-01 1 1.85 175.000 158.0054 155.5797 160.3095
#> 47 2012-06-01 11:30:00 2012-06-01 1 1.85 162.500 159.3458 157.0526 161.1047
#> 48 2012-06-01 11:45:00 2012-06-01 1 1.85 165.625 160.7277 158.5634 162.4647
#> 49 2012-06-01 12:00:00 2012-06-01 1 1.85 159.375 162.2002 160.1510 164.1497
#> 50 2012-06-01 12:15:00 2012-06-01 1 1.85 159.375 164.0740 162.0282 166.2938
#> 51 2012-06-01 12:30:00 2012-06-01 1 1.85 162.500 165.6557 163.5178 168.1274
#> 52 2012-06-01 12:45:00 2012-06-01 1 1.85 165.625 167.2160 164.9952 169.9521
#> 53 2012-06-01 13:00:00 2012-06-01 1 1.85 153.125 168.7745 166.5460 171.7842
#> 54 2012-06-01 13:15:00 2012-06-01 1 1.85 140.625 169.6355 167.3747 172.8035
#> 55 2012-06-01 13:30:00 2012-06-01 1 1.85 153.125 171.0881 168.7735 174.4969
#> 56 2012-06-01 13:45:00 2012-06-01 1 1.85 153.125 172.4370 170.0801 176.0689
#> 57 2012-06-01 14:00:00 2012-06-01 1 1.85 146.875 174.0277 171.4462 177.9163
#> 58 2012-06-01 14:15:00 2012-06-01 1 1.85 143.750 175.6071 172.6233 179.7471
#> 59 2012-06-01 14:30:00 2012-06-01 1 1.85 131.250 177.2261 173.7999 181.6251
#> 60 2012-06-01 14:45:00 2012-06-01 1 1.85 168.750 178.4056 174.7343 182.9782
#> 61 2012-06-01 15:00:00 2012-06-01 1 1.85 175.000 179.2437 175.4161 183.9356
#> 62 2012-06-01 15:15:00 2012-06-01 1 1.85 150.000 180.4956 176.4631 185.3485
#> 63 2012-06-01 15:30:00 2012-06-01 1 1.85 190.625 182.2572 177.9474 187.3224
#> 64 2012-06-01 15:45:00 2012-06-01 1 1.85 181.250 183.6345 179.0204 188.8803
#> 65 2012-06-01 16:00:00 2012-06-01 1 1.85 200.000 184.6039 179.8325 189.9585
#> 66 2012-06-01 16:15:00 2012-06-01 1 1.85 200.000 185.6549 180.7628 191.1090
#> 67 2012-06-01 16:30:00 2012-06-01 1 1.85 196.875 186.5096 181.4786 192.0542
#> 68 2012-06-01 16:45:00 2012-06-01 1 1.85 203.125 186.9396 181.8542 192.5207
#> 69 2012-06-01 17:00:00 2012-06-01 1 1.85 206.250 187.4099 182.2663 193.0298
#> 70 2012-06-01 17:15:00 2012-06-01 1 1.85 206.250 188.1034 182.8538 193.7891
#> 71 2012-06-01 17:30:00 2012-06-01 1 1.85 206.250 188.6005 183.2892 194.3237
#> 72 2012-06-01 17:45:00 2012-06-01 1 1.85 209.375 188.6086 183.3211 194.3162
#> 73 2012-06-01 18:00:00 2012-06-01 1 1.85 209.375 188.5256 183.2894 194.2035
#> 74 2012-06-01 18:15:00 2012-06-01 1 1.85 206.250 188.6583 183.4490 194.3238
#> 75 2012-06-01 18:30:00 2012-06-01 1 1.85 206.250 188.5367 183.3448 194.1820
#> 76 2012-06-01 18:45:00 2012-06-01 1 1.85 203.125 188.1724 183.0369 193.7744
#> 77 2012-06-01 19:00:00 2012-06-01 1 1.85 203.125 187.7099 182.6760 193.2488
#> 78 2012-06-01 19:15:00 2012-06-01 1 1.85 203.125 187.1669 182.2311 192.6415
#> 79 2012-06-01 19:30:00 2012-06-01 1 1.85 203.125 186.5392 181.7461 191.9323
#> 80 2012-06-01 19:45:00 2012-06-01 1 1.85 196.875 185.8228 181.1774 191.1287
#> 81 2012-06-01 20:00:00 2012-06-01 1 1.85 190.625 185.0887 180.6045 190.3033
#> 82 2012-06-01 20:15:00 2012-06-01 1 1.85 193.750 184.3134 179.9768 189.4386
#> 83 2012-06-01 20:30:00 2012-06-01 1 1.85 196.875 183.5295 179.3350 188.5668
#> 84 2012-06-01 20:45:00 2012-06-01 1 1.85 184.375 182.7656 178.7225 187.7145
#> 85 2012-06-01 21:00:00 2012-06-01 1 1.85 175.000 182.0113 178.1232 186.8720
#> 86 2012-06-01 21:15:00 2012-06-01 1 1.85 175.000 181.2683 177.5394 186.0415
#> 87 2012-06-01 21:30:00 2012-06-01 1 1.85 171.875 180.5435 176.9813 185.2295
#> 88 2012-06-01 21:45:00 2012-06-01 1 1.85 103.125 179.8355 176.4471 184.4340
#> 89 2012-06-01 22:00:00 2012-06-01 1 1.85 150.000 179.1411 175.9311 183.6531
#> 90 2012-06-01 22:15:00 2012-06-01 1 1.85 162.500 178.4414 175.4043 182.8700
#> 91 2012-06-01 22:30:00 2012-06-01 1 1.85 131.250 177.7537 174.8949 182.0980
#> 92 2012-06-01 22:45:00 2012-06-01 1 1.85 156.250 177.0818 174.2971 181.3449
#> 93 2012-06-01 23:00:00 2012-06-01 1 1.85 181.250 176.3702 173.5785 180.5507
#> 94 2012-06-01 23:15:00 2012-06-01 1 1.85 184.375 175.6662 172.8640 179.7671
#> 95 2012-06-01 23:30:00 2012-06-01 1 1.85 175.000 174.9048 172.1102 178.9240
#> 96 2012-06-01 23:45:00 2012-06-01 1 1.85 162.500 174.1385 171.3529 178.0762
#> dDO converge rsq a alo ahi
#> 1 NA Check convergence 0.3337845 NA NA NA
#> 2 -69.0845445 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 3 -65.6341784 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 4 -67.7908401 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 5 -68.6818929 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 6 -71.5087325 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 7 -70.6181749 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 8 -70.7349228 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 9 -70.5251236 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 10 -68.3168691 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 11 -70.2988904 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 12 -61.3975880 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 13 -70.9991111 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 14 -75.1375021 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 15 -71.8483676 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 16 -71.6808220 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 17 -67.0754081 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 18 -72.3179934 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 19 -63.9000233 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 20 -65.1629775 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 21 -66.3663545 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 22 -66.2378607 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 23 -39.6493899 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 24 -49.9162819 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 25 -64.6112712 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 26 -65.2113953 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 27 -63.8356181 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 28 -63.8299368 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 29 -61.1172233 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 30 -54.7187001 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 31 -27.4601952 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 32 21.9862620 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 33 41.0567243 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 34 -1.0084089 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 35 39.4182628 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 36 55.2455934 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 37 82.5644871 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 38 100.0281093 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 39 176.4600609 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 40 190.6623332 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 41 24.5619293 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 42 20.2840622 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 43 31.4164510 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 44 125.3838967 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 45 123.4716720 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 46 125.7862796 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 47 128.6860914 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 48 132.6619019 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 49 141.3552692 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 50 179.8844632 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 51 151.8478700 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 52 149.7855768 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 53 149.6143351 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 54 82.6617505 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 55 139.4506920 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 56 129.4872855 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 57 152.7074503 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 58 151.6205561 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 59 155.4270051 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 60 113.2374808 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 61 80.4529014 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 62 120.1851855 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 63 169.1147005 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 64 132.2185448 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 65 93.0623577 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 66 100.8942002 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 67 82.0507096 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 68 41.2762453 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 69 45.1545472 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 70 66.5740846 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 71 47.7220995 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 72 0.7781415 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 73 -7.9639075 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 74 12.7371610 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 75 -11.6712709 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 76 -34.9806159 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 77 -44.3937295 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 78 -52.1283680 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 79 -60.2605873 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 80 -68.7799893 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 81 -70.4723335 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 82 -74.4235308 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 83 -75.2547301 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 84 -73.3334668 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 85 -72.4149286 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 86 -71.3313843 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 87 -69.5795626 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 88 -67.9672993 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 89 -66.6643811 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 90 -67.1718490 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 91 -66.0131950 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 92 -64.5039541 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 93 -68.3105879 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 94 -67.5864931 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 95 -73.0927775 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> 96 -73.5705521 Check convergence 0.3337845 0.9122096 0.6136428 1.056313
#> b blo bhi P Plo Phi R
#> 1 NA NA NA NA NA NA NA
#> 2 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 3 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 4 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 5 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 6 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 7 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 8 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 9 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 10 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 11 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 12 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 13 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 14 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 15 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 16 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 17 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 18 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 19 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 20 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 21 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 22 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 23 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 24 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 25 0.3482113 0.2079293 0.4644247 1.366794 0.9194415 1.582709 146.9914
#> 26 0.3482113 0.2079293 0.4644247 4.761734 3.2032155 5.513954 146.9914
#> 27 0.3482113 0.2079293 0.4644247 9.589604 6.4509200 11.104490 146.9914
#> 28 0.3482113 0.2079293 0.4644247 13.778167 9.2685632 15.954727 146.9914
#> 29 0.3482113 0.2079293 0.4644247 18.760352 12.6200757 21.723956 146.9914
#> 30 0.3482113 0.2079293 0.4644247 25.969088 17.4693880 30.071469 146.9914
#> 31 0.3482113 0.2079293 0.4644247 80.596763 54.2173875 93.328770 146.9914
#> 32 0.3482113 0.2079293 0.4644247 125.260068 84.2623621 145.047613 146.9914
#> 33 0.3482113 0.2079293 0.4644247 148.164892 99.6704216 171.570751 146.9914
#> 34 0.3482113 0.2079293 0.4644247 61.329375 41.2562287 71.017680 146.9914
#> 35 0.3482113 0.2079293 0.4644247 177.176200 119.1863083 205.165024 146.9914
#> 36 0.3482113 0.2079293 0.4644247 207.201580 139.3843613 239.933565 146.9914
#> 37 0.3482113 0.2079293 0.4644247 230.855937 155.2966307 267.324640 146.9914
#> 38 0.3482113 0.2079293 0.4644247 252.107381 169.5924626 291.933210 146.9914
#> 39 0.3482113 0.2079293 0.4644247 259.338162 174.4566046 300.306251 146.9914
#> 40 0.3482113 0.2079293 0.4644247 254.686653 171.3275376 294.919935 146.9914
#> 41 0.3482113 0.2079293 0.4644247 37.873424 25.4774266 43.856353 146.9914
#> 42 0.3482113 0.2079293 0.4644247 98.629628 66.3480830 114.210317 146.9914
#> 43 0.3482113 0.2079293 0.4644247 151.846418 102.1469817 175.833854 146.9914
#> 44 0.3482113 0.2079293 0.4644247 331.844386 223.2314917 384.266406 146.9914
#> 45 0.3482113 0.2079293 0.4644247 354.661030 238.5802324 410.687434 146.9914
#> 46 0.3482113 0.2079293 0.4644247 371.591641 249.9694429 430.292602 146.9914
#> 47 0.3482113 0.2079293 0.4644247 378.447657 254.5814800 438.231674 146.9914
#> 48 0.3482113 0.2079293 0.4644247 383.319617 257.8588440 443.873265 146.9914
#> 49 0.3482113 0.2079293 0.4644247 391.432201 263.3161740 453.267409 146.9914
#> 50 0.3482113 0.2079293 0.4644247 406.312621 273.3262223 470.498514 146.9914
#> 51 0.3482113 0.2079293 0.4644247 329.485564 221.6447137 381.534957 146.9914
#> 52 0.3482113 0.2079293 0.4644247 338.149275 227.4727863 391.567289 146.9914
#> 53 0.3482113 0.2079293 0.4644247 375.008626 252.2680466 434.249374 146.9914
#> 54 0.3482113 0.2079293 0.4644247 247.433827 166.4485659 286.521367 146.9914
#> 55 0.3482113 0.2079293 0.4644247 333.828442 224.5661648 386.563886 146.9914
#> 56 0.3482113 0.2079293 0.4644247 322.144557 216.7064232 373.034278 146.9914
#> 57 0.3482113 0.2079293 0.4644247 364.272679 245.0459821 421.817451 146.9914
#> 58 0.3482113 0.2079293 0.4644247 365.088347 245.5946811 422.761971 146.9914
#> 59 0.3482113 0.2079293 0.4644247 380.431713 255.9161531 440.529155 146.9914
#> 60 0.3482113 0.2079293 0.4644247 290.950788 195.7223961 336.912776 146.9914
#> 61 0.3482113 0.2079293 0.4644247 236.741969 159.2561609 274.140499 146.9914
#> 62 0.3482113 0.2079293 0.4644247 292.560078 196.8049642 338.776289 146.9914
#> 63 0.3482113 0.2079293 0.4644247 365.088347 245.5946811 422.761971 146.9914
#> 64 0.3482113 0.2079293 0.4644247 332.726189 223.8246798 385.287508 146.9914
#> 65 0.3482113 0.2079293 0.4644247 258.412270 173.8337571 299.234093 146.9914
#> 66 0.3482113 0.2079293 0.4644247 261.454489 175.8802559 302.756897 146.9914
#> 67 0.3482113 0.2079293 0.4644247 243.818436 164.0164950 282.334847 146.9914
#> 68 0.3482113 0.2079293 0.4644247 179.733427 120.9065536 208.126221 146.9914
#> 69 0.3482113 0.2079293 0.4644247 185.597415 124.8512542 214.916553 146.9914
#> 70 0.3482113 0.2079293 0.4644247 220.847476 148.5639463 255.735126 146.9914
#> 71 0.3482113 0.2079293 0.4644247 190.755961 128.3214042 220.890003 146.9914
#> 72 0.3482113 0.2079293 0.4644247 117.456114 79.0126478 136.010856 146.9914
#> 73 0.3482113 0.2079293 0.4644247 101.693892 68.4094115 117.758648 146.9914
#> 74 0.3482113 0.2079293 0.4644247 131.983813 88.7854209 152.833520 146.9914
#> 75 0.3482113 0.2079293 0.4644247 103.435452 69.5809579 119.775326 146.9914
#> 76 0.3482113 0.2079293 0.4644247 66.972912 45.0526322 77.552736 146.9914
#> 77 0.3482113 0.2079293 0.4644247 46.933947 31.5724338 54.348182 146.9914
#> 78 0.3482113 0.2079293 0.4644247 37.586838 25.2846405 43.524495 146.9914
#> 79 0.3482113 0.2079293 0.4644247 18.583991 12.5014381 21.519736 146.9914
#> 80 0.3482113 0.2079293 0.4644247 7.076466 4.7603341 8.194348 146.9914
#> 81 0.3482113 0.2079293 0.4644247 2.072236 1.3939919 2.399591 146.9914
#> 82 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 83 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 84 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 85 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 86 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 87 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 88 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 89 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 90 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 91 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 92 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 93 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 94 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 95 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> 96 0.3482113 0.2079293 0.4644247 0.000000 0.0000000 0.000000 146.9914
#> Rlo Rhi NEM NEMlo NEMhi D Dlo
#> 1 NA NA NA NA NA NA NA
#> 2 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 19.184992 11.456044
#> 3 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 25.568170 15.283172
#> 4 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 21.578345 12.916049
#> 5 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 19.929898 11.942202
#> 6 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 14.700245 8.816710
#> 7 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 16.347776 9.811937
#> 8 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 16.131792 9.690760
#> 9 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 16.519921 9.930156
#> 10 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 20.605192 12.394603
#> 11 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 16.938452 10.197996
#> 12 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 33.405862 20.123851
#> 13 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 15.643044 9.437889
#> 14 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 7.987021 4.820844
#> 15 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 14.071920 8.496539
#> 16 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 14.381879 8.686655
#> 17 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 22.901895 13.837838
#> 18 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 13.203112 7.983256
#> 19 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 28.776357 17.404846
#> 20 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 26.439891 16.006751
#> 21 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 24.213644 14.673097
#> 22 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 24.451357 14.829521
#> 23 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 73.640028 44.676096
#> 24 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 54.646278 33.246091
#> 25 125.7794 161.9542 -145.624606 -160.3757064 -124.942140 26.093754 15.908978
#> 26 125.7794 161.9542 -142.229665 -156.4444029 -122.636636 21.588584 13.169302
#> 27 125.7794 161.9542 -137.401796 -150.8537830 -119.358028 19.305902 11.784664
#> 28 125.7794 161.9542 -133.213233 -146.0034735 -116.513574 15.127850 9.238406
#> 29 125.7794 161.9542 -128.231048 -140.2341579 -113.130172 15.164185 9.263508
#> 30 125.7794 161.9542 -121.022311 -131.8865200 -108.234717 19.792716 12.090840
#> 31 125.7794 161.9542 -66.394637 -71.9278469 -58.875118 15.593275 9.526820
#> 32 125.7794 161.9542 -21.731332 -41.2486175 -11.452055 62.405917 38.120730
#> 33 125.7794 161.9542 1.173492 -25.5152911 12.868064 74.781448 45.751676
#> 34 125.7794 161.9542 -85.662025 -90.9396964 -79.069114 83.796468 51.353649
#> 35 125.7794 161.9542 30.184800 -5.5874205 43.671989 42.738986 26.263335
#> 36 125.7794 161.9542 60.210180 11.5610655 77.978594 41.994167 25.823194
#> 37 125.7794 161.9542 83.864537 28.0257240 105.369809 68.879764 42.348851
#> 38 125.7794 161.9542 105.115981 42.5585873 129.978456 79.936021 49.225314
#> 39 125.7794 161.9542 112.346763 47.4795072 138.351516 214.104350 132.095415
#> 40 125.7794 161.9542 107.695254 44.3149348 132.965188 245.030063 152.361035
#> 41 125.7794 161.9542 -109.117975 -118.1014297 -100.150480 154.557545 97.067558
#> 42 125.7794 161.9542 -48.361772 -59.5410702 -39.727998 85.887287 54.273217
#> 43 125.7794 161.9542 4.855018 -22.9864504 16.777073 53.265416 33.751255
#> 44 125.7794 161.9542 184.852987 96.5576772 222.311786 47.107222 29.851795
#> 45 125.7794 161.9542 207.669630 111.9551259 248.732834 20.752963 13.168174
#> 46 125.7794 161.9542 224.600241 123.3737257 268.338015 8.104376 5.135325
#> 47 125.7794 161.9542 231.456257 127.9963761 276.277092 6.613012 4.182870
#> 48 125.7794 161.9542 236.328217 131.2808886 281.918686 9.096302 5.738452
#> 49 125.7794 161.9542 244.440801 136.7494587 291.312834 17.066447 10.740810
#> 50 125.7794 161.9542 259.321221 146.7782125 308.543948 73.465036 46.161045
#> 51 125.7794 161.9542 182.494164 94.9651196 219.580335 98.424395 61.942609
#> 52 125.7794 161.9542 191.157876 100.8136721 229.612676 85.945442 54.299494
#> 53 125.7794 161.9542 228.017227 125.6777030 272.294790 48.769293 30.900006
#> 54 125.7794 161.9542 100.442427 39.3728513 124.566598 52.481812 33.268589
#> 55 125.7794 161.9542 186.837043 97.8970907 224.609269 71.146738 45.109676
#> 56 125.7794 161.9542 175.153157 90.0077706 211.079649 64.398321 40.929482
#> 57 125.7794 161.9542 217.281279 118.4381542 259.862859 65.227504 41.528771
#> 58 125.7794 161.9542 218.096947 118.9882453 260.807380 62.401082 39.790210
#> 59 125.7794 161.9542 233.440313 129.3339982 278.574574 54.099646 34.545761
#> 60 125.7794 161.9542 143.959388 68.9189834 174.958105 65.529951 41.886169
#> 61 125.7794 161.9542 89.750570 32.0647391 112.185693 59.087298 37.934926
#> 62 125.7794 161.9542 145.568678 70.0081627 176.821620 76.773915 49.468617
#> 63 125.7794 161.9542 218.096947 118.9882453 260.807380 94.765249 61.363911
#> 64 125.7794 161.9542 185.734789 97.1529855 223.332890 58.869519 38.574760
#> 65 125.7794 161.9542 111.420870 46.8498657 137.279356 60.744492 39.785368
#> 66 125.7794 161.9542 114.463089 48.9182131 140.802168 72.191181 47.380180
#> 67 125.7794 161.9542 96.827036 36.9050985 120.380066 54.966777 36.240962
#> 68 125.7794 161.9542 32.742028 -3.8308604 46.387228 43.619026 28.908883
#> 69 125.7794 161.9542 38.606015 0.1689154 52.961329 44.929897 29.825400
#> 70 125.7794 161.9542 73.856077 21.1192471 93.780246 49.305980 32.716088
#> 71 125.7794 161.9542 43.764561 3.6720849 58.934868 44.521323 29.706466
#> 72 125.7794 161.9542 -29.535285 -46.6091541 -19.738217 30.974847 20.735349
#> 73 125.7794 161.9542 -45.297508 -57.4362267 -36.474392 30.564279 20.493300
#> 74 125.7794 161.9542 -15.007586 -36.6300761 -4.312848 38.571334 25.897152
#> 75 125.7794 161.9542 -43.555948 -56.2399488 -34.625220 21.964096 14.815259
#> 76 125.7794 161.9542 -80.018488 -84.4045425 -73.283126 15.304348 10.295891
#> 77 125.7794 161.9542 -100.057453 -107.6094444 -93.827904 17.929053 12.037363
#> 78 125.7794 161.9542 -109.404561 -118.4332930 -100.345100 12.967080 8.670688
#> 79 125.7794 161.9542 -128.407409 -140.4383815 -113.249938 16.925322 11.192210
#> 80 125.7794 161.9542 -139.914933 -153.7639687 -121.064701 12.671953 8.361323
#> 81 125.7794 161.9542 -144.919163 -159.5588122 -124.463074 14.545346 9.559458
#> 82 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 9.307868 6.112307
#> 83 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 7.770149 5.086926
#> 84 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 11.324486 7.383315
#> 85 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 13.023782 8.468334
#> 86 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 15.028339 9.739544
#> 87 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 18.269209 11.831649
#> 88 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 21.251896 13.788213
#> 89 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 23.662295 15.335747
#> 90 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 22.723479 14.619778
#> 91 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 24.866989 16.099923
#> 92 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 27.659085 17.794543
#> 93 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 20.616812 13.345937
#> 94 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 21.956387 14.069231
#> 95 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 11.769761 7.562453
#> 96 125.7794 161.9542 -146.991400 -161.9584390 -125.870330 10.885878 6.975261
#> Dhi
#> 1 NA
#> 2 25.588138
#> 3 33.999706
#> 4 28.604665
#> 5 26.343637
#> 6 19.378750
#> 7 21.489896
#> 8 21.141481
#> 9 21.599198
#> 10 26.872279
#> 11 22.035419
#> 12 43.369190
#> 13 20.253777
#> 14 10.322325
#> 15 18.139004
#> 16 18.506487
#> 17 29.418386
#> 18 16.931801
#> 19 36.841164
#> 20 33.793166
#> 21 30.883015
#> 22 31.124038
#> 23 93.700092
#> 24 69.360132
#> 25 33.031759
#> 26 27.296986
#> 27 24.364516
#> 28 19.063125
#> 29 19.080005
#> 30 24.888858
#> 31 19.597742
#> 32 78.445652
#> 33 93.997373
#> 34 105.416893
#> 35 53.681244
#> 36 52.802206
#> 37 86.878299
#> 38 100.988909
#> 39 271.109245
#> 40 310.206309
#> 41 195.373578
#> 42 108.132663
#> 43 67.003289
#> 44 59.387971
#> 45 26.291640
#> 46 10.346402
#> 47 8.514495
#> 48 11.823195
#> 49 22.399000
#> 50 97.392758
#> 51 131.722581
#> 52 115.770093
#> 53 66.192921
#> 54 72.016400
#> 55 98.130375
#> 56 89.641770
#> 57 91.629004
#> 58 88.675694
#> 59 77.833370
#> 60 95.666245
#> 61 87.301785
#> 62 114.402461
#> 63 142.817612
#> 64 90.845533
#> 65 94.792888
#> 66 113.555126
#> 67 87.263760
#> 68 70.172776
#> 69 72.591760
#> 70 79.746598
#> 71 72.976756
#> 72 51.170102
#> 73 50.567878
#> 74 63.802299
#> 75 36.648751
#> 76 25.376662
#> 77 29.547728
#> 78 21.137058
#> 79 27.002144
#> 80 20.022324
#> 81 22.708235
#> 82 14.419606
#> 83 11.920978
#> 84 17.191550
#> 85 19.595733
#> 86 22.394713
#> 87 27.053588
#> 88 31.355624
#> 89 34.655486
#> 90 32.821695
#> 91 35.944392
#> 92 39.517930
#> 93 29.445249
#> 94 30.956877
#> 95 16.554990
#> 96 15.229995