Introduction
The sptotal package was developed for predicting a
weighted sum, most commonly a mean or total, from a finite number of
sample units in a fixed geographic area. Estimating totals and means
from a finite population is an important goal for both academic research
and management of environmental data. One naturally turns to classical
sampling methods, such as simple random sampling or stratified random
sampling. Classical sampling methods depend on probability-based sample
designs and are robust. Very few assumptions are required because the
probability distribution for inference comes from the sample design,
which is known and under our control. For design-based methods, sample
plots are chosen at random, they are measured or counted, and inference
is obtained from the probability of sampling those units randomly based
on the design (e.g., Horwitz-Thompson estimation). As an alternative, we
will use model-based methods, specifically geostatistics, to accomplish
the same goals. Geostatistics does not rely on a specific sampling
design. Instead, when using geostatistics, we assume the data were
produced by a stochastic process with parameters that can be estimated.
The relevant theory is given by Ver Hoef (2008). The
sptotal package puts much of the code and plots in Ver Hoef
(2008) in easily accessible, convenient functions.
In the sptotal package, our goal is to estimate some
linear function of all of the sample units, call it \(\tau(\mathbf{z}) = \mathbf{b}^\prime
\mathbf{z}\), where \(\mathbf{z}\) is a vector of the realized
values for all the sample units and \(\mathbf{b}\) is a vector of weights. By
“realized,” we mean that whatever processes produced the data have
already happened, and that, if we had enough resources, we could measure
them all, obtaining a complete census. If \(\tau(\mathbf{z})\) is a population total,
then every element of \(\mathbf{b}\)
contains a \(1\). Generally, \(\mathbf{b}\) can contain any set of weights
that we would like to multiply times each value in a population, and
then these are summed, yielding a weighted sum.
The vector \(\mathbf{b}\) contains the weights that we would apply if we could measure or count every observation, but, because of cost consideration, we usually only have a sample.
Data
Prior to using the sptotal package, the data needs to be
in R in the proper format. For this package, we assume that
your data set is a data.frame() object, described
below.
Data Frame Structure
Data input for the sptotal package is a
data.frame. The basic information required to fit a spatial
linear model, and make predictions, are the response variable,
covariates, the x- and y-coordinates, and a column of weights. You can
envision your whole population of possible samples as a
data.frame organized as follows,
where the red rectangle represents the column of the response variable, and the top part, colored in red, are observed locations, and the lower part, colored in white, are the unobserved values. To the right, colored in blue, are possibly several columns containing covariates thought to be predictive for the response value at each location. Covariates must be known for both observed and unobserved locations, and the covariates for unobserved locations are shown as pale blue below the darker blue covariates for observed locations above. It is also possible that there are no available covariates.
The data.frame must have x- and y-coordinates, and they
are shown as two columns colored in green, with the coordinates for the
unobserved locations shown as pale green below the darker green
coordinates for the observed locations above. The
data.frame can have a column of weights. If one is not
provided, we assume a column of all ones so that the prediction is for
the population total. The column of weights is purple, with weights for
the observed locations a darker shade, above the lighter shade of purple
representing weights for unsampled locations. Finally, the
data.frame may contain columns that are not relevant to
predicting the weighted sum. These columns are represented by the orange
color, with the sampled locations a darker shade, above the unsampled
locations with the lighter shade.
Of course, the data do not have to be in exactly this order, either in terms of rows or columns. Sampled and unsampled rows can be intermingled, and columns of response variable, covariates, coordinates, and weights can be also be intermingled. The figure above is an idealized graphic of the data. However, this figure helps envision how the data are used and illustrate the goal. We desire a weighted sum, where the weights (in the purple column) are multiplied with the response variable (red/white) column, and then summed. Because some of the response values are unknown (the white values in the response column), covariates and spatial information (obtained from the x- and y-coordinates) are used to predict the unobserved (white) values. The weights (purple) are then applied to both the observed response values (red), and the predicted response values (white), to obtain a weighted sum. Because we use predictions for unobserved response values, it is important to assess our uncertainty, and the software provides both an estimate of the weighted sum, mean, or total for the response variable as well as its estimated prediction variance.
Simulated Data Creation
To demonstrate the package, we created some simulated data so they are perfectly behaved, and we know exactly how they were produced. Here, we give a brief description before using the main features of the package. To get started, install the package
install.packages("sptotal")and then type
library(sptotal)Type
data(simdata)and then simdata will be available in your workspace. To
see the first six observations of simdata, type
head(simdata)
#> x y X1 X2 X3 X4 X5
#> 1 0.025 0.975 -0.8460525 0.11866907 -0.2123901 0.38430607 0.08154129
#> 2 0.025 0.925 -0.6583116 -0.07686491 -0.9001410 -1.24774376 1.46631630
#> 3 0.025 0.875 0.2222961 -0.22803942 0.2820468 0.20560677 0.48713665
#> 4 0.025 0.825 -0.5433925 0.56894993 -0.9839629 -0.04950434 -0.78195604
#> 5 0.025 0.775 -0.7550155 -0.72592167 -0.4217208 0.26767033 0.40493269
#> 6 0.025 0.725 -0.1786784 0.33452155 -1.2134533 2.18704575 -0.54903128
#> X6 X7 F1 F2 Z wts1 wts2
#> 1 1.0747592 -0.0252824 3 3 15.94380 0.0025 0
#> 2 0.1299263 1.4651052 2 5 15.04616 0.0025 0
#> 3 -0.2537515 0.2682010 2 3 14.52765 0.0025 0
#> 4 -0.3259937 0.7858140 2 5 12.13401 0.0025 0
#> 5 -1.2284475 1.2944342 2 2 11.75260 0.0025 0
#> 6 -1.0366099 0.7938890 1 4 11.58142 0.0025 0simdata is a data frame with 400 observations. The
spatial coordinates are numeric variables in columns named
x and y. We created 7 continuous covariates,
X1 through X7. The variables X1
through X5 were all created using the rnorm()
function, so they are all standard normal variates that are independent
between and within variable. Variables X6 and
X7 were independent from each other, but spatially
autocorrelated within, each with a variance parameter of 1, an
autocorrelation range parameter of 0.2 from an exponential model, and a
small nugget effect of 0.01. The variables F1 and
F2 are factor variables with 3 and 5 levels, respectively.
The variable Z is the response. Data were simulated from
the model
\[\begin{align*} Z_i = 10 & + 0 \cdot X1_i + 0.1 \cdot X2_i + 0.2 \cdot X3_i + 0.3 \cdot X4_i + \\ & 0.4 \cdot X5_i + 0.4 \cdot X6_i + 0.1 \cdot X7_i + F1_i + F2_i + \delta_i + \varepsilon_i \end{align*}\]
where factor levels for F1 have effects \(0, 0.4, 0.8\), and factor levels for
F2 have effects \(0, 0.1, 0.2,
0.3, 0.4\). The random errors \(\{\delta_i\}\) are spatially autocorrelated
from an exponential model,
\[ \textrm{cov}(\delta_i,\delta_j) = 2*\exp(-d_{i,j}) \]
where \(d_{i,j}\) is Euclidean
distance between locations \(i\) and
\(j\). In geostatistics terminology,
this model has a partial sill of 2 and a range of 1. The random errors
\(\{\varepsilon_i\}\) are independent
with variance 0.02, and this variance is called the nugget effect. Two
columns with weights are included, wts1 contains 1/400 for
each row, so the weighted sum will yield a prediction of the overall
mean. The column wts2 contains a 1 for 25 locations, and 0
elsewhere, so the weighted sum will be a prediction of a total in the
subset of 25 locations.
The spatial locations of simdata are in a \(20 \times 20\) grid uniformly spaced in a
box with sides of length 1,
require(ggplot2)
ggplot(data = simdata, aes(x = x, y = y)) + geom_point(size = 3) +
geom_point(data = subset(simdata, wts2 == 1), colour = "red",
size = 3)
The locations of the 25 sites where wts2 is equal to one
are shown in red.
We have simulated the data for the whole population. This is
convenient, because we know the true means and totals. In order to
compare with the prediction from the sptotal package, let’s
find the true population total
sum(simdata[ ,'Z'])
#> [1] 4834.326as well as the total in the subset of 25 sites
sum(simdata[ ,'wts2'] * simdata[ ,'Z'])
#> [1] 273.3751However, we will now sample from this population to provide a more
realistic setting where we can measure only a part of the whole
population. In order to make results reproducible, we use the
set.seed command, along with sample. The code
below will replace some of the response values with NA to
represent the unsampled sites.
set.seed(1)
# take a random sample of 100
obsID <- sample(1:nrow(simdata), 100)
simobs <- simdata
simobs$Z <- NA
simobs[obsID, 'Z'] <- simdata[obsID, 'Z']We now have a data set where the whole population is known,
simdata, and another one, simobs, where 75% of
the response variable of the population has been replaced by
NA. Next we show the sampled sites as solid circles, while
the missing values are shown as open circles, and we use red again to
show the sites within the small area of 25 locations.
ggplot(data = simobs, aes(x = x, y = y)) +
geom_point(shape = 1, size = 2.5, stroke = 1.5) +
geom_point(data = subset(simobs, !is.na(Z)), shape = 16, size = 3.5) +
geom_point(data = subset(simobs, !is.na(Z) & wts2 == 1), shape = 16,
colour = "red", size = 3.5) +
geom_point(data = subset(simobs, is.na(Z) & wts2 == 1), shape = 1,
colour = "red", size = 2.5, stroke = 1.5)
We will use the simobs data to illustrate use of the
sptotal package.
Using the sptotal Package
After your data is in a similar format to simobs, using
the sptotal package occurs in two primary stages. In the
first, we fit a spatial linear model. This stage estimates spatial
regression coefficients and spatial autocorrelation parameters. In the
second stage, we predict the unsampled locations for the response value,
and create a prediction for the weighted sum (e.g. the total) of all
response variable values, both observed and predicted. To show how the
package works, we demonstrate on ideal, simulated data. Then, we give a
realistic example on moose data and a second example on lakes data to
provide further insight and documentation. The moose example also has a
section on data preparation steps.
Fitting a Spatial Linear Model: slmfit
We continue with our use of the simulated data, simobs,
to illustrate fitting the spatial linear model. The spatial
model-fitting function is slmfit
(spatial-linear-model-fit), which uses a formula like many other
model-fitting functions in R (e.g., the lm()
function). To fit a basic spatial linear model we use
slmfit_out1 <- slmfit(formula = Z ~ X1 + X2 + X3 + X4 + X5 +
X6 + X7 + F1 + F2,
data = simobs, xcoordcol = 'x',
ycoordcol = 'y',
CorModel = "Exponential")The documentation describes the arguments in more detail, but as
mentioned earlier, the linear model includes a formula argument, and the
data.frame that is being used as a data set. We also need
to include which columns contain the \(x\)- and \(y\)-coordinates, which are arguments to
xcoordcol and ycoordcol, respectively. In the
above example, we specify 'x' and 'y' as the
column coordinates arguments since the names of the coordinate columns
in our simulated data set are 'x' and 'y'. We
also need to specify a spatial autocorrelation model, which is given by
the CorModel argument. As with many other linear model
fits, we can obtain a summary of the model fit,
summary(slmfit_out1)
#>
#> Call:
#> Z ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + F1 + F2
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.9390 -0.6271 0.3338 1.2520 2.8137
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 11.36965 1.03775 10.956 < 2e-16 ***
#> X1 -0.05596 0.06400 -0.874 0.38437
#> X2 0.02661 0.06606 0.403 0.68814
#> X3 0.18292 0.06469 2.828 0.00583 **
#> X4 0.26487 0.05741 4.613 1e-05 ***
#> X5 0.38434 0.06022 6.382 < 2e-16 ***
#> X6 0.47612 0.11198 4.252 5e-05 ***
#> X7 0.02893 0.11761 0.246 0.80625
#> F12 0.29596 0.15154 1.953 0.05407 .
#> F13 0.70853 0.13136 5.394 < 2e-16 ***
#> F22 0.15384 0.17073 0.901 0.37008
#> F23 0.19804 0.17828 1.111 0.26973
#> F24 0.25492 0.20024 1.273 0.20641
#> F25 0.39748 0.23691 1.678 0.09703 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Covariance Parameters:
#> Exponential Model
#> Nugget 1.009265e-06
#> Partial Sill 2.930385e+00
#> Range 5.891474e-01
#>
#> Generalized R-squared: 0.5996812The output looks similar to the summary of a standard
lm object, but there is some extra output at the end that
gives our fitted covariance parameters. Plotting
slmfit_out1 gives a semi-variogram of the residuals along
with the fitted model:
plot(slmfit_out1)
Note that the fitted curve may not appear to fit the empirical variogram perfectly for a couple of reasons. First, only pairs of points that have a distance between 0 and one-half the maximum distance are shown. Second, the fitted model is estimated using REML, which may give different results than using weighted least squares.
We can also examine a histogram of the residuals as well as a histogram of the cross-validation (leave-one-out) residuals:
residraw <- residuals(slmfit_out1)
qplot(residraw, bins = 20) + xlab("Residuals")
#> Warning: `qplot()` was deprecated in ggplot2 3.4.0.
residcv <- residuals(slmfit_out1, cross.validation = TRUE)
qplot(residcv, bins = 20) + xlab("CV Residuals")
There is still one somewhat large cross-validation residual for an observed count that is larger than what would be predicted from a model without that particular count. The cause of this somewhat large residual can be attributed to random chance because we know that the data was simulated to follow all assumptions.
Prediction: predict
After we have obtained a fitted spatial linear model, we can use the
predict() function to construct a data frame of predictions
for the unsampled sites. By default, the predict() function
assumes that we are predicting the population total and outputs this
predicted total, the prediction variance for the total, a 90% prediction
interval for the total, and some basic summary information about the
number of sites sampled, the total number of units counted, etc. We name
this object pred_obj in the chunk below and also construct
a 90% confidence interval for the total.
pred_obj <- predict(slmfit_out1, conf_level = 0.90)
pred_objWe predict a total of 4817 units in this simulated region with 90% confidence bounds of (4779, 4856). The prediction interval is fairly small because we simulated data that were highly correlated, increasing precision in prediction for unobserved sites. We can see that the prediction of the total is close to the true value of 4834.326, and the true value is within the prediction interval.
To access the data.frame that was input into
slmfit, but is now appended with site-by-site predictions
and site-by-site prediction variances, we can use
pred_obj$Pred_df. This data set might be particularly
useful if you would like to generate your own map with site-by-site
predictions using other tools. The site-by-site predictions for density
are given by the variable name_of_response_pred_density
while the site-by-site predictions for counts are given by
name_of_response_pred_count. These two columns will only
differ if you have provided a column for areas of each site.
prediction_df <- pred_obj$Pred_df
head(prediction_df[ ,c("x", "y", "Z", "Z_pred_density")])Examining results: plot()
Finally, to get a basic plot of the predictions, we can use the
plot() function.
plot(pred_obj)
The map shows the distribution of the response across sampled and
unsampled sites. Its purpose is simply to give the user a very quick
idea of the distribution of the response. For example, we see from the
plot that the predicted response is low in the upper-right region of the
graph, is high in the middle of the region and in the upper-left corner
of the region, and is low again at the lower portion of the area of
interest. However, using the prediction data frame generated from the
predict() function, you can use ggplot2 or any
other plotting package to construct your own map that may be more useful
in your context.
Prediction for a Small Area of Interest
Spatial prediction can be used to estimate means and totals over finite populations from geographic regions, but can also be used for the special case of estimating a mean or total in a small area of interest. The term small area estimation refers to making an inference on a smaller geographic area within the overall study area. There may be few or no samples within that small area, so that estimation by classical sampling methods may not be possible or variances become exceedingly large.
If we want to predict a quantity other than the population total,
then we need to specify the column in our data set that has the
appropriate prediction weights in a wtscol argument. For
example, we might want to predict the total for a small area of
interest. if we want to predict the total for the 25 sites in coloured
in red, then we can use
pred_obj2 <- predict(slmfit_out1, wtscol = "wts2")
print(pred_obj2)
#> Prediction Info:
#> Prediction SE 90% LB 90% UB
#> Z 282.2 7.342 270.1 294.3
#> Numb. Sites Sampled Total Numb. Sites Total Observed Average Density
#> Z 100 400 1220 12.2Recall that the true total for this small area was 273.4. We see that this is close to our prediction of 282.2 and is also within the bounds of our prediction interval.
Real Data Examples
Moose Abundance from Aerial Surveys
The simulated data example assumes that the coordinates are a
Transverse Mercator projection (TM), that the vector of the response is
numeric and has NA values for sites that were not sampled,
and that the areas of each site sampled are all the same. For this
example, we consider a data set on moose abundance in Alaska obtained
from Alaska
Department of Fish and Game, Division of Wildlife Conservation. Each
observation corresponds to a moose counted at a particular site, but
operational constraints do not permit all sites to be counted. We begin
by loading the data into R.
data(AKmoose_df)
AKmoose_df
#> elev_mean strat surveyed total x y lon lat
#> 0 560.3333 L 0 NA 38.98384825 1.301806e+02 -147.8750 63.71667
#> 1 620.4167 L 0 NA 34.86652773 1.302284e+02 -147.9583 63.71667
#> 2 468.9167 L 1 0 30.74963291 1.302815e+02 -148.0417 63.71667
#> 3 492.7500 L 0 NA 26.63241710 1.303400e+02 -148.1250 63.71667
#> 4 379.5833 L 0 NA 22.51526115 1.304038e+02 -148.2083 63.71667
#> 5 463.7500 L 0 NA 38.94319469 1.264665e+02 -147.8750 63.68333
#> 6 456.4375 L 0 NA 34.82103091 1.265143e+02 -147.9583 63.68333
#> 7 358.9375 L 0 NA 30.69929374 1.265674e+02 -148.0417 63.68333
#> 8 333.1875 L 0 NA 26.57723416 1.266260e+02 -148.1250 63.68333
#> 9 257.8750 L 0 NA 22.45523537 1.266899e+02 -148.2083 63.68333
#> 10 417.6250 L 0 NA 38.90255070 1.227521e+02 -147.8750 63.65000
#> 11 362.3125 L 1 0 34.77554479 1.228000e+02 -147.9583 63.65000
#> 12 265.7500 L 0 NA 30.64896544 1.228532e+02 -148.0417 63.65000
#> 13 269.3125 L 0 NA 26.52206419 1.229118e+02 -148.1250 63.65000
#> 14 225.0000 L 0 NA 22.39522272 1.229758e+02 -148.2083 63.65000
#> 15 172.7500 M 1 0 18.26882464 1.230451e+02 -148.2917 63.65000
#> 16 398.6250 L 0 NA 38.86191861 1.190378e+02 -147.8750 63.61666
#> 17 279.6250 L 1 0 34.73007200 1.190857e+02 -147.9583 63.61666
#> 18 227.8750 L 0 NA 30.59865236 1.191390e+02 -148.0417 63.61666
#> 19 197.8750 L 0 NA 26.46691037 1.191976e+02 -148.1250 63.61666
#> 20 194.7500 L 0 NA 22.33522813 1.192616e+02 -148.2083 63.61666
#> 21 167.9375 M 0 NA 18.20398971 1.193311e+02 -148.2917 63.61666
#> 22 204.0000 L 0 NA 14.07244432 1.194059e+02 -148.3750 63.61666
#> 23 619.6000 L 1 0 47.09442203 1.152440e+02 -147.7083 63.58333
#> 24 479.7500 L 0 NA 42.95803072 1.152812e+02 -147.7917 63.58333
#> 25 350.5000 L 0 NA 38.82130074 1.153237e+02 -147.8750 63.58333
#> 26 286.4167 L 0 NA 34.68461462 1.153716e+02 -147.9583 63.58333
#> 27 207.5833 L 0 NA 30.54835739 1.154250e+02 -148.0417 63.58333
#> 28 181.5833 L 0 NA 26.41177586 1.154837e+02 -148.1250 63.58333
#> 29 174.3333 L 0 NA 22.27525505 1.155478e+02 -148.2083 63.58333
#> 30 164.5833 M 0 NA 18.13917747 1.156172e+02 -148.2917 63.58333
#> 31 188.4000 L 0 NA 14.00279297 1.156921e+02 -148.3750 63.58333
#> 32 515.0500 L 0 NA 47.06349078 1.115299e+02 -147.7083 63.55000
#> 33 358.8750 L 0 NA 42.92226236 1.115671e+02 -147.7917 63.55000
#> 34 364.1250 L 0 NA 38.78069481 1.116096e+02 -147.8750 63.55000
#> 35 217.5625 L 0 NA 34.63917159 1.116576e+02 -147.9583 63.55000
#> 36 191.5625 L 0 NA 30.49807620 1.117110e+02 -148.0417 63.55000
#> 37 172.6250 L 0 NA 26.35665755 1.117697e+02 -148.1250 63.55000
#> 38 162.0625 M 0 NA 22.21529857 1.118339e+02 -148.2083 63.55000
#> 39 164.5625 L 0 NA 18.07438426 1.119034e+02 -148.2917 63.55000
#> 40 167.5500 L 0 NA 13.93316208 1.119784e+02 -148.3750 63.55000
#> 41 543.8750 L 0 NA 67.76480465 1.077107e+02 -147.2917 63.51667
#> 42 577.3125 L 0 NA 63.61824587 1.077209e+02 -147.3750 63.51667
#> 43 593.1875 L 0 NA 59.47169973 1.077365e+02 -147.4583 63.51667
#> 44 612.0000 L 0 NA 55.32555017 1.077575e+02 -147.5417 63.51667
#> 45 630.5625 L 0 NA 51.17904516 1.077839e+02 -147.6250 63.51667
#> 46 455.8500 L 0 NA 47.03256864 1.078158e+02 -147.7083 63.51667
#> 47 319.5625 L 0 NA 42.88650452 1.078530e+02 -147.7917 63.51667
#> 48 289.2500 L 0 NA 38.74010081 1.078956e+02 -147.8750 63.51667
#> 49 211.6875 L 0 NA 34.59374144 1.079436e+02 -147.9583 63.51667
#> 50 181.8125 L 0 NA 30.44781080 1.079970e+02 -148.0417 63.51667
#> 51 164.1250 M 1 0 26.30155543 1.080558e+02 -148.1250 63.51667
#> 52 163.5000 M 1 0 22.15536074 1.081200e+02 -148.2083 63.51667
#> 53 174.9375 L 0 NA 18.00961012 1.081896e+02 -148.2917 63.51667
#> 54 186.3500 L 1 0 13.86355163 1.082646e+02 -148.3750 63.51667
#> 55 503.6923 L 0 NA 76.06048918 1.039922e+02 -147.1250 63.48333
#> 56 620.5000 L 0 NA 71.90908579 1.039916e+02 -147.2083 63.48333
#> 57 466.6667 L 0 NA 67.75806458 1.039965e+02 -147.2917 63.48333
#> 58 447.9375 L 0 NA 63.60667113 1.040067e+02 -147.3750 63.48333
#> 59 597.9375 L 0 NA 59.45529032 1.040223e+02 -147.4583 63.48333
#> 60 655.8750 L 0 NA 55.30430652 1.040434e+02 -147.5417 63.48333
#> 61 566.3750 L 0 NA 51.15296682 1.040698e+02 -147.6250 63.48333
#> 62 507.7000 L 0 NA 47.00165560 1.041017e+02 -147.7083 63.48333
#> 63 375.7500 L 0 NA 42.85075722 1.041389e+02 -147.7917 63.48333
#> 64 261.4375 L 0 NA 38.69951878 1.041815e+02 -147.8750 63.48333
#> 65 198.4375 L 0 NA 34.54832466 1.042296e+02 -147.9583 63.48333
#> 66 173.5000 M 0 NA 30.39755970 1.042831e+02 -148.0417 63.48333
#> 67 158.6250 M 0 NA 26.24646955 1.043419e+02 -148.1250 63.48333
#> 68 170.1667 L 0 NA 22.09544005 1.044062e+02 -148.2083 63.48333
#> 69 190.5714 L 0 NA 17.94485504 1.044758e+02 -148.2917 63.48333
#> 70 219.0769 L 0 NA 13.79396170 1.045509e+02 -148.3750 63.48333
#> 71 434.9375 L 0 NA 84.37549449 1.002954e+02 -146.9583 63.45000
#> 72 347.5000 L 0 NA 80.21965006 1.002840e+02 -147.0417 63.45000
#> 73 406.3750 L 0 NA 76.06341713 1.002780e+02 -147.1250 63.45000
#> 74 482.6500 L 0 NA 71.90718051 1.002774e+02 -147.2083 63.45000
#> 75 354.3750 L 0 NA 67.75132649 1.002823e+02 -147.2917 63.45000
#> 76 458.6667 L 0 NA 63.59509981 1.002925e+02 -147.3750 63.45000
#> 77 656.5833 L 0 NA 59.43888574 1.003082e+02 -147.4583 63.45000
#> 78 583.9167 L 0 NA 55.28306963 1.003292e+02 -147.5417 63.45000
#> 79 549.4167 L 0 NA 51.12689618 1.003557e+02 -147.6250 63.45000
#> 80 384.0667 L 0 NA 46.97075167 1.003876e+02 -147.7083 63.45000
#> 81 285.6667 L 0 NA 42.81502044 1.004248e+02 -147.7917 63.45000
#> 82 218.3333 L 0 NA 38.65894871 1.004675e+02 -147.8750 63.45000
#> 83 178.7500 L 0 NA 34.50292126 1.005156e+02 -147.9583 63.45000
#> 84 164.2500 M 0 NA 30.34732291 1.005691e+02 -148.0417 63.45000
#> 85 160.0000 M 0 NA 26.19139991 1.006280e+02 -148.1250 63.45000
#> 86 171.1875 L 0 NA 22.03553651 1.006924e+02 -148.2083 63.45000
#> 87 202.7000 L 0 NA 17.88011903 1.007621e+02 -148.2917 63.45000
#> 88 213.3750 L 0 NA 13.72439227 1.008372e+02 -148.3750 63.45000
#> 89 425.2500 L 0 NA 92.71015129 9.662025e+01 -146.7917 63.41667
#> 90 422.3125 L 0 NA 88.54912778 9.659803e+01 -146.8750 63.41667
#> 91 419.7500 L 0 NA 84.38808476 9.658122e+01 -146.9583 63.41667
#> 92 362.3125 L 1 0 80.22740946 9.656983e+01 -147.0417 63.41667
#> 93 298.5625 L 0 NA 76.06634422 9.656384e+01 -147.1250 63.41667
#> 94 370.1500 L 0 NA 71.90527628 9.656327e+01 -147.2083 63.41667
#> 95 361.0625 L 0 NA 67.74459040 9.656811e+01 -147.2917 63.41667
#> 96 499.3750 L 0 NA 63.58353190 9.657836e+01 -147.3750 63.41667
#> 97 567.0000 L 0 NA 59.42248602 9.659402e+01 -147.4583 63.41667
#> 98 430.5000 L 1 0 55.26183802 9.661510e+01 -147.5417 63.41667
#> 99 423.7500 L 0 NA 51.10083322 9.664159e+01 -147.6250 63.41667
#> 100 315.4500 L 0 NA 46.93985688 9.667349e+01 -147.7083 63.41667
#> 101 239.8750 L 0 NA 42.77929423 9.671080e+01 -147.7917 63.41667
#> 102 210.0625 L 0 NA 38.61839062 9.675352e+01 -147.8750 63.41667
#> 103 161.7500 M 1 0 34.45753079 9.680166e+01 -147.9583 63.41667
#> 104 167.3750 M 1 5 30.29710196 9.685521e+01 -148.0417 63.41667
#> 105 171.7500 L 0 NA 26.13634651 9.691417e+01 -148.1250 63.41667
#> 106 176.5625 L 0 NA 21.97565167 9.697854e+01 -148.2083 63.41667
#> 107 206.0500 L 0 NA 17.81540216 9.704832e+01 -148.2917 63.41667
#> 108 191.6875 L 0 NA 13.65484337 9.712352e+01 -148.3750 63.41667
#> 109 626.5555 L 0 NA 126.05677151 9.327908e+01 -146.1250 63.38334
#> 110 554.2222 L 1 7 121.89125903 9.321350e+01 -146.2083 63.38334
#> 111 318.1250 L 0 NA 117.72606674 9.315335e+01 -146.2917 63.38334
#> 112 238.8750 L 0 NA 113.56043764 9.309861e+01 -146.3750 63.38334
#> 113 242.3750 L 0 NA 109.39475788 9.304928e+01 -146.4583 63.38334
#> 114 388.3125 L 0 NA 105.22941315 9.300537e+01 -146.5417 63.38334
#> 115 332.3333 L 0 NA 101.06364792 9.296688e+01 -146.6250 63.38334
#> 116 369.0667 L 0 NA 96.89784735 9.293381e+01 -146.7083 63.38334
#> 117 347.8333 L 0 NA 92.73239864 9.290615e+01 -146.7917 63.38334
#> 118 296.5000 L 0 NA 88.56654473 9.288391e+01 -146.8750 63.38334
#> 119 291.3571 L 0 NA 84.40067131 9.286709e+01 -146.9583 63.38334
#> 120 287.1250 L 0 NA 80.23516557 9.285568e+01 -147.0417 63.38334
#> 121 287.1250 L 0 NA 76.06927044 9.284969e+01 -147.1250 63.38334
#> 122 388.1500 L 0 NA 71.90337162 9.284912e+01 -147.2083 63.38334
#> 123 469.2500 L 0 NA 67.73785630 9.285396e+01 -147.2917 63.38334
#> 124 471.3750 L 0 NA 63.57196741 9.286422e+01 -147.3750 63.38334
#> 125 362.5625 L 0 NA 59.40609114 9.287990e+01 -147.4583 63.38334
#> 126 362.6875 L 0 NA 55.24061368 9.290099e+01 -147.5417 63.38334
#> 127 401.3125 L 0 NA 51.07477798 9.292750e+01 -147.6250 63.38334
#> 128 401.9000 L 0 NA 46.90897122 9.295943e+01 -147.7083 63.38334
#> 129 229.0000 L 0 NA 42.74357858 9.299677e+01 -147.7917 63.38334
#> 130 162.1250 L 0 NA 38.57784452 9.303954e+01 -147.8750 63.38334
#> 131 197.0625 M 0 NA 34.41215472 9.308772e+01 -147.9583 63.38334
#> 132 190.3750 L 0 NA 30.24689485 9.314131e+01 -148.0417 63.38334
#> 133 183.4375 L 0 NA 26.08130940 9.320032e+01 -148.1250 63.38334
#> 134 187.6875 L 0 NA 21.91578353 9.326475e+01 -148.2083 63.38334
#> 135 191.0000 L 0 NA 17.75070439 9.333459e+01 -148.2917 63.38334
#> 136 189.4375 L 0 NA 13.58531502 9.340986e+01 -148.3750 63.38334
#> 137 604.0833 L 0 NA 126.11764670 8.956511e+01 -146.1250 63.35000
#> 138 558.4500 L 0 NA 121.94730484 8.949947e+01 -146.2083 63.35000
#> 139 304.8125 L 0 NA 117.77728363 8.943927e+01 -146.2917 63.35000
#> 140 257.7500 L 0 NA 113.60682519 8.938448e+01 -146.3750 63.35000
#> 141 205.5625 L 0 NA 109.43631612 8.933511e+01 -146.4583 63.35000
#> 142 247.3750 L 0 NA 105.26614253 8.929116e+01 -146.5417 63.35000
#> 143 199.6875 L 0 NA 101.09554802 8.925264e+01 -146.6250 63.35000
#> 144 250.0000 L 1 0 96.92491868 8.921953e+01 -146.7083 63.35000
#> 145 248.8750 L 0 NA 92.75464066 8.919186e+01 -146.7917 63.35000
#> 146 245.4375 L 0 NA 88.58395751 8.916960e+01 -146.8750 63.35000
#> 147 232.1429 L 0 NA 84.41325535 8.915276e+01 -146.9583 63.35000
#> 148 300.6667 L 0 NA 80.24292082 8.914134e+01 -147.0417 63.35000
#> 149 398.0000 L 0 NA 76.07219596 8.913535e+01 -147.1250 63.35000
#> 150 483.8667 L 0 NA 71.90146842 8.913477e+01 -147.2083 63.35000
#> 151 435.9167 L 0 NA 67.73112381 8.913962e+01 -147.2917 63.35000
#> 152 403.0000 L 0 NA 63.56040569 8.914989e+01 -147.3750 63.35000
#> 153 293.9167 L 0 NA 59.38970019 8.916558e+01 -147.4583 63.35000
#> 154 318.8333 L 0 NA 55.21939343 8.918669e+01 -147.5417 63.35000
#> 155 376.8333 L 0 NA 51.04872897 8.921323e+01 -147.6250 63.35000
#> 156 369.8000 L 0 NA 46.87809295 8.924518e+01 -147.7083 63.35000
#> 157 171.9167 M 1 0 42.70787147 8.928256e+01 -147.7917 63.35000
#> 158 171.6667 M 0 NA 38.53730812 8.932536e+01 -147.8750 63.35000
#> 159 219.0833 L 0 NA 34.36678901 8.937358e+01 -147.9583 63.35000
#> 160 203.5000 L 0 NA 30.19670025 8.942722e+01 -148.0417 63.35000
#> 161 192.3333 L 0 NA 26.02628544 8.948628e+01 -148.1250 63.35000
#> 162 183.0833 L 0 NA 21.85593020 8.955077e+01 -148.2083 63.35000
#> 163 181.8000 L 0 NA 17.68602210 8.962067e+01 -148.2917 63.35000
#> 164 195.7500 L 0 NA 13.51580329 8.969600e+01 -148.3750 63.35000
#> 165 478.5000 L 0 NA 134.52825666 8.599880e+01 -145.9583 63.31667
#> 166 346.7500 L 0 NA 130.35360672 8.592227e+01 -146.0417 63.31667
#> 167 386.2500 L 0 NA 126.17850383 8.585115e+01 -146.1250 63.31667
#> 168 301.4615 L 0 NA 122.00333452 8.578546e+01 -146.2083 63.31667
#> 169 191.5000 L 0 NA 117.82848533 8.572520e+01 -146.2917 63.31667
#> 170 171.0769 L 0 NA 113.65319898 8.567036e+01 -146.3750 63.31667
#> 171 144.5000 L 0 NA 109.47786203 8.562095e+01 -146.4583 63.31667
#> 172 153.8750 L 0 NA 105.30286102 8.557697e+01 -146.5417 63.31667
#> 173 152.1250 L 0 NA 101.12743866 8.553841e+01 -146.6250 63.31667
#> 174 170.3889 L 0 NA 96.95198099 8.550528e+01 -146.7083 63.31667
#> 175 177.0000 L 0 NA 92.77687608 8.547758e+01 -146.7917 63.31667
#> 176 179.6875 L 1 0 88.60136512 8.545530e+01 -146.8750 63.31667
#> 177 246.0000 L 0 NA 84.42583516 8.543844e+01 -146.9583 63.31667
#> 178 334.1250 L 0 NA 80.25067327 8.542702e+01 -147.0417 63.31667
#> 179 412.1250 L 0 NA 76.07512062 8.542102e+01 -147.1250 63.31667
#> 180 496.7222 L 0 NA 71.89956478 8.542044e+01 -147.2083 63.31667
#> 181 452.1111 L 0 NA 67.72439332 8.542530e+01 -147.2917 63.31667
#> 182 343.0625 L 0 NA 63.54884740 8.543557e+01 -147.3750 63.31667
#> 183 298.1250 L 0 NA 59.37331409 8.545128e+01 -147.4583 63.31667
#> 184 226.0625 L 0 NA 55.19817996 8.547241e+01 -147.5417 63.31667
#> 185 227.0000 L 0 NA 51.02268769 8.549896e+01 -147.6250 63.31667
#> 186 195.9000 L 0 NA 46.84722383 8.553095e+01 -147.7083 63.31667
#> 187 148.8125 M 0 NA 42.67217495 8.556836e+01 -147.7917 63.31667
#> 188 217.8125 M 1 0 38.49678374 8.561119e+01 -147.8750 63.31667
#> 189 251.2500 L 0 NA 34.32143675 8.565946e+01 -147.9583 63.31667
#> 190 189.3750 L 0 NA 30.14652104 8.571314e+01 -148.0417 63.31667
#> 191 174.6875 L 0 NA 25.97127781 8.577226e+01 -148.1250 63.31667
#> 192 174.2222 L 0 NA 21.79609511 8.583680e+01 -148.2083 63.31667
#> 193 182.7778 L 0 NA 17.62135899 8.590676e+01 -148.2917 63.31667
#> 194 194.5625 L 0 NA 13.44631218 8.598216e+01 -148.3750 63.31667
#> 195 452.7500 L 0 NA 134.59874437 8.228521e+01 -145.9583 63.28333
#> 196 259.8125 L 1 0 130.41926857 8.220860e+01 -146.0417 63.28333
#> 197 237.2500 L 0 NA 126.23933941 8.213742e+01 -146.1250 63.28333
#> 198 186.4375 L 0 NA 122.05934335 8.207168e+01 -146.2083 63.28333
#> 199 141.8500 L 0 NA 117.87966888 8.201137e+01 -146.2917 63.28333
#> 200 116.3333 L 0 NA 113.69955635 8.195648e+01 -146.3750 63.28333
#> 201 122.6667 L 0 NA 109.51939322 8.190703e+01 -146.4583 63.28333
#> 202 127.0000 L 0 NA 105.33956650 8.186301e+01 -146.5417 63.28333
#> 203 149.3333 L 0 NA 101.15931799 8.182442e+01 -146.6250 63.28333
#> 204 151.5000 L 0 NA 96.97903420 8.179126e+01 -146.7083 63.28333
#> 205 151.4500 L 0 NA 92.79910363 8.176353e+01 -146.7917 63.28333
#> 206 169.8125 L 0 NA 88.61876656 8.174123e+01 -146.8750 63.28333
#> 207 247.7500 L 0 NA 84.43841000 8.172436e+01 -146.9583 63.28333
#> 208 356.5625 L 0 NA 80.25842247 8.171293e+01 -147.0417 63.28333
#> 209 390.8125 L 0 NA 76.07804424 8.170692e+01 -147.1250 63.28333
#> 210 450.8750 L 0 NA 71.89766231 8.170635e+01 -147.2083 63.28333
#> 211 345.1000 L 0 NA 67.71766521 8.171120e+01 -147.2917 63.28333
#> 212 300.9375 L 0 NA 63.53729320 8.172149e+01 -147.3750 63.28333
#> 213 268.5000 L 0 NA 59.35693381 8.173721e+01 -147.4583 63.28333
#> 214 188.1250 L 0 NA 55.17697452 8.175835e+01 -147.5417 63.28333
#> 215 177.0000 L 0 NA 50.99665564 8.178493e+01 -147.6250 63.28333
#> 216 147.5000 M 1 6 46.81636566 8.181695e+01 -147.7083 63.28333
#> 217 165.5000 M 0 NA 42.63649108 8.185439e+01 -147.7917 63.28333
#> 218 281.9375 L 0 NA 38.45627372 8.189726e+01 -147.8750 63.28333
#> 219 231.5625 L 0 NA 34.27610056 8.194556e+01 -147.9583 63.28333
#> 220 175.1250 L 1 5 30.09635860 8.199929e+01 -148.0417 63.28333
#> 221 168.3125 L 1 2 25.91628966 8.205846e+01 -148.1250 63.28333
#> 222 174.5500 L 0 NA 21.73628023 8.212306e+01 -148.2083 63.28333
#> 223 187.1875 L 0 NA 17.55671878 8.219308e+01 -148.2917 63.28333
#> 224 189.7500 L 0 NA 13.37684567 8.226854e+01 -148.3750 63.28333
#> 225 405.5833 M 0 NA 134.66921114 7.857162e+01 -145.9583 63.25000
#> 226 344.1333 M 0 NA 130.48491091 7.849495e+01 -146.0417 63.25000
#> 227 165.3750 L 0 NA 126.30015691 7.842371e+01 -146.1250 63.25000
#> 228 129.9375 M 1 0 122.11533654 7.835791e+01 -146.2083 63.25000
#> 229 130.0000 M 0 NA 117.93083723 7.829755e+01 -146.2917 63.25000
#> 230 108.2778 M 0 NA 113.74589993 7.824261e+01 -146.3750 63.25000
#> 231 111.4375 M 1 0 109.56091207 7.819312e+01 -146.4583 63.25000
#> 232 119.3750 L 0 NA 105.37626106 7.814906e+01 -146.5417 63.25000
#> 233 132.1875 L 0 NA 101.19118786 7.811044e+01 -146.6250 63.25000
#> 234 133.7857 L 0 NA 97.00607937 7.807725e+01 -146.7083 63.25000
#> 235 137.0667 L 0 NA 92.82132456 7.804950e+01 -146.7917 63.25000
#> 236 208.2500 L 0 NA 88.63616283 7.802718e+01 -146.8750 63.25000
#> 237 306.2500 L 0 NA 84.45098212 7.801030e+01 -146.9583 63.25000
#> 238 393.6667 L 0 NA 80.26617037 7.799885e+01 -147.0417 63.25000
#> 239 328.0000 L 1 0 76.08096699 7.799284e+01 -147.1250 63.25000
#> 240 329.0625 L 0 NA 71.89576041 7.799226e+01 -147.2083 63.25000
#> 241 279.5500 L 0 NA 67.71093910 7.799712e+01 -147.2917 63.25000
#> 242 245.0000 L 0 NA 63.52574244 7.800742e+01 -147.3750 63.25000
#> 243 261.4375 L 0 NA 59.34055839 7.802315e+01 -147.4583 63.25000
#> 244 182.8750 L 0 NA 55.15577438 7.804432e+01 -147.5417 63.25000
#> 245 153.5000 M 0 NA 50.97063132 7.807092e+01 -147.6250 63.25000
#> 246 135.9000 M 0 NA 46.78551666 7.810296e+01 -147.7083 63.25000
#> 247 202.2500 M 1 0 42.60081782 7.814043e+01 -147.7917 63.25000
#> 248 297.0000 L 0 NA 38.41577574 7.818334e+01 -147.8750 63.25000
#> 249 229.4375 L 0 NA 34.23077785 7.823169e+01 -147.9583 63.25000
#> 250 166.9375 M 1 0 30.04621207 7.828547e+01 -148.0417 63.25000
#> 251 176.5000 L 0 NA 25.86131785 7.834468e+01 -148.1250 63.25000
#> 252 181.3000 L 0 NA 21.67648411 7.840934e+01 -148.2083 63.25000
#> 253 184.0000 L 0 NA 17.49209777 7.847942e+01 -148.2917 63.25000
#> 254 187.8333 L 0 NA 13.30739981 7.855495e+01 -148.3750 63.25000
#> 255 241.3333 L 0 NA 9.12277713 7.863591e+01 -148.4583 63.25000
#> 256 328.5000 L 0 NA 4.93861863 7.872230e+01 -148.5417 63.25000
#> 257 266.4167 L 1 3 0.75416383 7.881413e+01 -148.6250 63.25000
#> 258 262.5882 L 1 0 134.73965692 7.485806e+01 -145.9583 63.21667
#> 259 262.0000 L 0 NA 130.55053370 7.478132e+01 -146.0417 63.21667
#> 260 202.5833 L 0 NA 126.36095628 7.471002e+01 -146.1250 63.21667
#> 261 107.8333 M 0 NA 122.17131206 7.464416e+01 -146.2083 63.21667
#> 262 107.8750 M 1 0 117.98199034 7.458375e+01 -146.2917 63.21667
#> 263 120.4500 L 1 0 113.79222970 7.452877e+01 -146.3750 63.21667
#> 264 114.0625 L 0 NA 109.60241855 7.447923e+01 -146.4583 63.21667
#> 265 116.4375 L 0 NA 105.41294470 7.443513e+01 -146.5417 63.21667
#> 266 120.3750 L 0 NA 101.22304821 7.439648e+01 -146.6250 63.21667
#> 267 124.3750 L 0 NA 97.03311649 7.436326e+01 -146.7083 63.21667
#> 268 158.2632 L 0 NA 92.84353888 7.433548e+01 -146.7917 63.21667
#> 269 260.1765 L 0 NA 88.65355391 7.431315e+01 -146.8750 63.21667
#> 270 324.4375 L 0 NA 84.46354948 7.429625e+01 -146.9583 63.21667
#> 271 405.5000 L 0 NA 80.27391496 7.428479e+01 -147.0417 63.21667
#> 272 250.0000 L 0 NA 76.08388886 7.427878e+01 -147.1250 63.21667
#> 273 229.2500 L 0 NA 71.89385908 7.427820e+01 -147.2083 63.21667
#> 274 196.0000 L 0 NA 67.70421500 7.428307e+01 -147.2917 63.21667
#> 275 147.5833 L 0 NA 63.51419513 7.429337e+01 -147.3750 63.21667
#> 276 136.4167 L 0 NA 59.32418785 7.430912e+01 -147.4583 63.21667
#> 277 134.1667 M 0 NA 55.13458156 7.433030e+01 -147.5417 63.21667
#> 278 132.6667 M 0 NA 50.94461476 7.435693e+01 -147.6250 63.21667
#> 279 160.2000 M 0 NA 46.75467684 7.438899e+01 -147.7083 63.21667
#> 280 330.1667 L 0 NA 42.56515519 7.442650e+01 -147.7917 63.21667
#> 281 290.5000 L 0 NA 38.37528983 7.446944e+01 -147.8750 63.21667
#> 282 181.0000 M 1 0 34.18546863 7.451783e+01 -147.9583 63.21667
#> 283 167.9167 M 1 0 29.99607947 7.457165e+01 -148.0417 63.21667
#> 284 180.4167 L 0 NA 25.80636242 7.463092e+01 -148.1250 63.21667
#> 285 191.2667 L 0 NA 21.61670480 7.469563e+01 -148.2083 63.21667
#> 286 190.0833 L 0 NA 17.42749601 7.476578e+01 -148.2917 63.21667
#> 287 200.5625 L 1 1 13.23797464 7.484137e+01 -148.3750 63.21667
#> 288 285.3750 L 0 NA 9.04852898 7.492240e+01 -148.4583 63.21667
#> 289 271.7500 L 0 NA 4.85954693 7.500886e+01 -148.5417 63.21667
#> 290 280.2353 L 0 NA 0.67026862 7.510077e+01 -148.6250 63.21667
#> 291 300.6250 L 0 NA 139.00433264 7.122676e+01 -145.8750 63.18333
#> 292 164.2000 L 1 0 134.81008168 7.114451e+01 -145.9583 63.18333
#> 293 136.6875 M 0 NA 130.61613690 7.106771e+01 -146.0417 63.18333
#> 294 123.7500 M 1 3 126.42173754 7.099635e+01 -146.1250 63.18333
#> 295 105.9375 M 0 NA 122.22727186 7.093043e+01 -146.2083 63.18333
#> 296 110.3333 L 0 NA 118.03312817 7.086996e+01 -146.2917 63.18333
#> 297 119.0000 L 0 NA 113.83854566 7.081494e+01 -146.3750 63.18333
#> 298 120.0000 L 0 NA 109.64391263 7.076535e+01 -146.4583 63.18333
#> 299 129.0000 L 0 NA 105.44961738 7.072122e+01 -146.5417 63.18333
#> 300 130.0000 L 0 NA 101.25489908 7.068253e+01 -146.6250 63.18333
#> 301 144.6250 L 0 NA 97.06014553 7.064928e+01 -146.7083 63.18333
#> 302 244.2500 L 1 0 92.86574656 7.062149e+01 -146.7917 63.18333
#> 303 275.7500 L 0 NA 88.67093981 7.059913e+01 -146.8750 63.18333
#> 304 295.2500 L 0 NA 84.47611409 7.058222e+01 -146.9583 63.18333
#> 305 263.6250 L 0 NA 80.28165824 7.057075e+01 -147.0417 63.18333
#> 306 187.8750 L 0 NA 76.08680987 7.056473e+01 -147.1250 63.18333
#> 307 170.0625 L 0 NA 71.89195832 7.056416e+01 -147.2083 63.18333
#> 308 142.4000 L 0 NA 67.69749290 7.056902e+01 -147.2917 63.18333
#> 309 126.8750 L 0 NA 63.50265126 7.057934e+01 -147.3750 63.18333
#> 310 123.6875 L 0 NA 59.30782220 7.059510e+01 -147.4583 63.18333
#> 311 126.8125 M 1 3 55.11339406 7.061630e+01 -147.5417 63.18333
#> 312 131.0000 M 0 NA 50.91860596 7.064295e+01 -147.6250 63.18333
#> 313 232.6000 L 0 NA 46.72384624 7.067504e+01 -147.7083 63.18333
#> 314 380.7500 L 0 NA 42.52950320 7.071258e+01 -147.7917 63.18333
#> 315 297.4375 L 0 NA 38.33481600 7.075556e+01 -147.8750 63.18333
#> 316 171.6875 M 0 NA 34.14017295 7.080399e+01 -147.9583 63.18333
#> 317 175.0000 M 0 NA 29.94596285 7.085786e+01 -148.0417 63.18333
#> 318 179.5625 M 0 NA 25.75142338 7.091718e+01 -148.1250 63.18333
#> 319 196.1500 M 0 NA 21.55694434 7.098194e+01 -148.2083 63.18333
#> 320 200.4375 L 0 NA 17.36291353 7.105215e+01 -148.2917 63.18333
#> 321 243.1875 L 0 NA 13.16857015 7.112780e+01 -148.3750 63.18333
#> 322 227.5000 L 0 NA 8.97430199 7.120890e+01 -148.4583 63.18333
#> 323 229.8750 L 0 NA 4.78049882 7.129544e+01 -148.5417 63.18333
#> 324 251.5000 L 1 0 0.58639840 7.138743e+01 -148.6250 63.18333
#> 325 210.6923 L 0 NA 139.07956127 6.751309e+01 -145.8750 63.15000
#> 326 152.5556 L 0 NA 134.88048894 6.743077e+01 -145.9583 63.15000
#> 327 116.6667 M 0 NA 130.68172427 6.735390e+01 -146.0417 63.15000
#> 328 103.5625 M 1 2 126.48250411 6.728248e+01 -146.1250 63.15000
#> 329 104.8750 L 0 NA 122.28321715 6.721650e+01 -146.2083 63.15000
#> 330 113.6250 L 0 NA 118.08425366 6.715598e+01 -146.2917 63.15000
#> 331 125.1250 L 1 0 113.88485043 6.710091e+01 -146.3750 63.15000
#> 332 160.5500 L 0 NA 109.68539669 6.705129e+01 -146.4583 63.15000
#> 333 214.3333 L 0 NA 105.48628120 6.700712e+01 -146.5417 63.15000
#> 334 155.9167 L 0 NA 101.28674224 6.696839e+01 -146.6250 63.15000
#> 335 184.8333 L 1 9 97.08716855 6.693512e+01 -146.7083 63.15000
#> 336 210.3333 L 0 NA 92.88794888 6.690730e+01 -146.7917 63.15000
#> 337 310.2632 L 0 NA 88.68832150 6.688492e+01 -146.8750 63.15000
#> 338 234.4375 L 0 NA 84.48867517 6.686799e+01 -146.9583 63.15000
#> 339 152.8125 L 0 NA 80.28939915 6.685652e+01 -147.0417 63.15000
#> 340 146.3125 L 0 NA 76.08973017 6.685049e+01 -147.1250 63.15000
#> 341 143.1250 L 0 NA 71.89005851 6.684992e+01 -147.2083 63.15000
#> 342 125.1000 M 0 NA 67.69077243 6.685479e+01 -147.2917 63.15000
#> 343 120.0000 M 1 4 63.49111018 6.686511e+01 -147.3750 63.15000
#> 344 121.0625 M 0 NA 59.29146051 6.688088e+01 -147.4583 63.15000
#> 345 127.2500 L 0 NA 55.09221218 6.690210e+01 -147.5417 63.15000
#> 346 173.5000 L 0 NA 50.89260345 6.692878e+01 -147.6250 63.15000
#> 347 354.5000 L 0 NA 46.69302308 6.696090e+01 -147.7083 63.15000
#> 348 323.5625 L 0 NA 42.49385982 6.699847e+01 -147.7917 63.15000
#> 349 185.3125 M 1 2 38.29435194 6.704149e+01 -147.8750 63.15000
#> 350 182.2500 L 1 2 34.09488820 6.708996e+01 -147.9583 63.15000
#> 351 186.7500 L 0 NA 29.89585732 6.714387e+01 -148.0417 63.15000
#> 352 186.8125 L 0 NA 25.69649761 6.720324e+01 -148.1250 63.15000
#> 353 209.7000 M 1 0 21.49719730 6.726806e+01 -148.2083 63.15000
#> 354 220.9375 M 0 NA 17.29834664 6.733833e+01 -148.2917 63.15000
#> 355 232.9375 L 0 NA 13.09918243 6.741405e+01 -148.3750 63.15000
#> 356 227.0625 L 1 0 8.90009391 6.749522e+01 -148.4583 63.15000
#> 357 237.2500 L 0 NA 4.70146979 6.758183e+01 -148.5417 63.15000
#> 358 278.6316 L 0 NA 0.50254843 6.767390e+01 -148.6250 63.15000
#> 359 223.0000 L 0 NA 139.15476741 6.379943e+01 -145.8750 63.11666
#> 360 178.8333 L 0 NA 134.95087615 6.371704e+01 -145.9583 63.11666
#> 361 117.8667 M 1 0 130.74729203 6.364011e+01 -146.0417 63.11666
#> 362 103.2500 M 0 NA 126.54325250 6.356862e+01 -146.1250 63.11666
#> 363 105.3125 L 0 NA 122.33914621 6.350259e+01 -146.2083 63.11666
#> 364 112.2500 L 0 NA 118.13536385 6.344202e+01 -146.2917 63.11666
#> 365 124.4375 L 0 NA 113.93114134 6.338690e+01 -146.3750 63.11666
#> 366 264.4000 L 0 NA 109.72686835 6.333724e+01 -146.4583 63.11666
#> 367 339.3750 L 0 NA 105.52293406 6.329303e+01 -146.5417 63.11666
#> 368 162.0625 L 0 NA 101.31857587 6.325427e+01 -146.6250 63.11666
#> 369 192.5000 L 0 NA 97.11418247 6.322097e+01 -146.7083 63.11666
#> 370 215.9375 L 0 NA 92.91014455 6.319312e+01 -146.7917 63.11666
#> 371 207.0625 L 0 NA 88.70569800 6.317073e+01 -146.8750 63.11666
#> 372 187.6667 L 0 NA 84.50123198 6.315379e+01 -146.9583 63.11666
#> 373 126.2500 L 0 NA 80.29713723 6.314230e+01 -147.0417 63.11666
#> 374 119.5833 M 0 NA 76.09264960 6.313627e+01 -147.1250 63.11666
#> 375 120.1667 M 0 NA 71.88815827 6.313569e+01 -147.2083 63.11666
#> 376 120.0000 M 0 NA 67.68405397 6.314057e+01 -147.2917 63.11666
#> 377 120.0000 M 1 0 63.47957255 6.315090e+01 -147.3750 63.11666
#> 378 120.9333 M 1 2 59.27510371 6.316669e+01 -147.4583 63.11666
#> 379 128.5625 M 1 0 55.07103714 6.318793e+01 -147.5417 63.11666
#> 380 224.0000 L 0 NA 50.86660872 6.321462e+01 -147.6250 63.11666
#> 381 271.8500 L 0 NA 46.66220915 6.324677e+01 -147.7083 63.11666
#> 382 170.7500 L 0 NA 42.45822711 6.328437e+01 -147.7917 63.11666
#> 383 168.1875 M 1 3 38.25390000 6.332743e+01 -147.8750 63.11666
#> 384 215.0625 L 0 NA 34.04961700 6.337594e+01 -147.9583 63.11666
#> 385 184.9333 L 0 NA 29.84576728 6.342990e+01 -148.0417 63.11666
#> 386 207.8333 L 0 NA 25.64158827 6.348932e+01 -148.1250 63.11666
#> 387 214.0667 M 0 NA 21.43746864 6.355420e+01 -148.2083 63.11666
#> 388 220.5833 M 0 NA 17.23379906 6.362452e+01 -148.2917 63.11666
#> 389 231.2500 L 1 0 13.02981546 6.370030e+01 -148.3750 63.11666
#> 390 242.5833 L 0 NA 8.82590753 6.378154e+01 -148.4583 63.11666
#> 391 257.5000 L 0 NA 4.62246439 6.386823e+01 -148.5417 63.11666
#> 392 318.3750 L 0 NA 0.41872354 6.396038e+01 -148.6250 63.11666
#> 393 192.5625 L 0 NA 139.22994674 6.008600e+01 -145.8750 63.08333
#> 394 148.0625 L 1 0 135.02123777 6.000354e+01 -145.9583 63.08333
#> 395 104.7895 M 0 NA 130.81283641 5.992654e+01 -146.0417 63.08333
#> 396 103.5385 M 0 NA 126.60397923 5.985500e+01 -146.1250 63.08333
#> 397 107.9167 L 0 NA 122.39505533 5.978891e+01 -146.2083 63.08333
#> 398 118.6667 L 0 NA 118.18645582 5.972829e+01 -146.2917 63.08333
#> 399 124.1875 L 0 NA 113.97741575 5.967312e+01 -146.3750 63.08333
#> 400 177.1667 L 0 NA 109.76832521 5.962342e+01 -146.4583 63.08333
#> 401 179.7778 L 0 NA 105.55957384 5.957917e+01 -146.5417 63.08333
#> 402 181.1875 L 0 NA 101.35039815 5.954038e+01 -146.6250 63.08333
#> 403 187.7500 L 0 NA 97.14118777 5.950705e+01 -146.7083 63.08333
#> 404 156.7500 L 0 NA 92.93233231 5.947918e+01 -146.7917 63.08333
#> 405 214.7778 L 0 NA 88.72306829 5.945677e+01 -146.8750 63.08333
#> 406 153.7222 M 0 NA 84.51378482 5.943981e+01 -146.9583 63.08333
#> 407 106.6250 M 1 0 80.30487357 5.942832e+01 -147.0417 63.08333
#> 408 105.9375 M 1 3 76.09556798 5.942228e+01 -147.1250 63.08333
#> 409 116.2500 M 0 NA 71.88625972 5.942170e+01 -147.2083 63.08333
#> 410 120.0556 M 0 NA 67.67733791 5.942658e+01 -147.2917 63.08333
#> 411 125.0556 L 0 NA 63.46803904 5.943692e+01 -147.3750 63.08333
#> 412 126.3846 L 0 NA 59.25875274 5.945272e+01 -147.4583 63.08333
#> 413 130.2500 M 1 0 55.04986865 5.947398e+01 -147.5417 63.08333
#> 414 141.2500 M 0 NA 50.84062326 5.950070e+01 -147.6250 63.08333
#> 415 142.5333 M 0 NA 46.63140621 5.953287e+01 -147.7083 63.08333
#> 416 143.9167 M 1 0 42.42260711 5.957050e+01 -147.7917 63.08333
#> 417 194.5000 L 0 NA 38.21346248 5.961360e+01 -147.8750 63.08333
#> 418 180.2500 L 0 NA 34.00436143 5.966215e+01 -147.9583 63.08333
#> 419 185.6923 L 0 NA 29.79569561 5.971616e+01 -148.0417 63.08333
#> 420 200.2778 L 0 NA 25.58669851 5.977563e+01 -148.1250 63.08333
#> 421 217.0556 L 0 NA 21.37776177 5.984056e+01 -148.2083 63.08333
#> 422 228.7500 M 1 0 17.16927449 5.991094e+01 -148.2917 63.08333
#> 423 242.5000 L 0 NA 12.96047322 5.998679e+01 -148.3750 63.08333
#> 424 259.5000 L 0 NA 8.75174708 6.006810e+01 -148.4583 63.08333
#> 425 309.6111 L 0 NA 4.54348714 6.015486e+01 -148.5417 63.08333
#> 426 400.0000 L 0 NA 0.33492851 6.024709e+01 -148.6250 63.08333
#> 427 167.0625 L 0 NA 139.30510350 5.637259e+01 -145.8750 63.05000
#> 428 108.4375 M 1 7 135.09157827 5.629006e+01 -145.9583 63.05000
#> 429 103.2500 M 1 15 130.87836111 5.621300e+01 -146.0417 63.05000
#> 430 103.8500 M 1 2 126.66468773 5.614139e+01 -146.1250 63.05000
#> 431 118.0000 L 1 0 122.45094766 5.607525e+01 -146.2083 63.05000
#> 432 150.2500 L 1 0 118.23753245 5.601458e+01 -146.2917 63.05000
#> 433 159.2500 L 1 5 114.02367626 5.595936e+01 -146.3750 63.05000
#> 434 139.8333 L 1 1 109.80976963 5.590961e+01 -146.4583 63.05000
#> 435 177.8000 L 1 2 105.59620262 5.586533e+01 -146.5417 63.05000
#> 436 276.1333 L 1 3 101.38221087 5.582651e+01 -146.6250 63.05000
#> 437 134.1875 L 1 0 97.16818394 5.579315e+01 -146.7083 63.05000
#> 438 163.4375 L 1 2 92.95451340 5.576525e+01 -146.7917 63.05000
#> 439 207.7500 L 1 3 88.74043337 5.574282e+01 -146.8750 63.05000
#> 440 117.0500 M 0 NA 84.52633389 5.572585e+01 -146.9583 63.05000
#> 441 110.1875 M 0 NA 80.31260657 5.571435e+01 -147.0417 63.05000
#> 442 109.0625 M 0 NA 76.09848549 5.570831e+01 -147.1250 63.05000
#> 443 119.3750 M 1 0 71.88436072 5.570773e+01 -147.2083 63.05000
#> 444 123.1875 L 1 0 67.67062386 5.571261e+01 -147.2917 63.05000
#> 445 129.1500 L 0 NA 63.45650899 5.572296e+01 -147.3750 63.05000
#> 446 133.3750 L 0 NA 59.24240669 5.573878e+01 -147.4583 63.05000
#> 447 134.1875 L 0 NA 55.02870753 5.576005e+01 -147.5417 63.05000
#> 448 133.9375 L 0 NA 50.81464561 5.578679e+01 -147.6250 63.05000
#> 449 138.3000 L 0 NA 46.60061252 5.581899e+01 -147.7083 63.05000
#> 450 165.5000 L 0 NA 42.38699780 5.585666e+01 -147.7917 63.05000
#> 451 179.3750 L 0 NA 38.17303710 5.589979e+01 -147.8750 63.05000
#> 452 173.8125 L 0 NA 33.95912047 5.594838e+01 -147.9583 63.05000
#> 453 185.0625 L 0 NA 29.74563796 5.600243e+01 -148.0417 63.05000
#> 454 201.5500 L 0 NA 25.53182523 5.606196e+01 -148.1250 63.05000
#> 455 221.3125 M 0 NA 21.31807182 5.612694e+01 -148.2083 63.05000
#> 456 236.1875 M 1 0 17.10476929 5.619739e+01 -148.2917 63.05000
#> 457 252.8125 M 1 0 12.89115180 5.627330e+01 -148.3750 63.05000
#> 458 276.7500 M 1 0 8.67760990 5.635468e+01 -148.4583 63.05000
#> 459 306.8500 M 0 NA 4.46453360 5.644151e+01 -148.5417 63.05000
#> 460 405.1250 M 0 NA 0.25115864 5.653381e+01 -148.6250 63.05000
#> 461 114.6667 M 0 NA 139.38023772 5.265920e+01 -145.8750 63.01667
#> 462 111.1429 M 1 16 135.16189766 5.257660e+01 -145.9583 63.01667
#> 463 127.7500 M 1 3 130.94386615 5.249947e+01 -146.0417 63.01667
#> 464 104.8947 M 1 13 126.72537802 5.242780e+01 -146.1250 63.01667
#> 465 215.5294 M 1 4 122.50682372 5.236161e+01 -146.2083 63.01667
#> 466 204.8750 L 1 8 118.28859375 5.230088e+01 -146.2917 63.01667
#> 467 196.6875 L 1 7 114.06992288 5.224562e+01 -146.3750 63.01667
#> 468 151.8750 L 1 3 109.85120160 5.219583e+01 -146.4583 63.01667
#> 469 135.7000 M 1 0 105.63282040 5.215151e+01 -146.5417 63.01667
#> 470 126.3846 M 1 2 101.41401405 5.211265e+01 -146.6250 63.01667
#> 471 150.1667 M 1 4 97.19517252 5.207926e+01 -146.7083 63.01667
#> 472 176.0833 L 1 4 92.97668784 5.205135e+01 -146.7917 63.01667
#> 473 145.1667 M 1 1 88.75779323 5.202889e+01 -146.8750 63.01667
#> 474 114.8000 M 0 NA 84.53887970 5.201191e+01 -146.9583 63.01667
#> 475 115.3125 L 0 NA 80.32033826 5.200040e+01 -147.0417 63.01667
#> 476 115.6875 L 0 NA 76.10140212 5.199435e+01 -147.1250 63.01667
#> 477 119.6875 M 0 NA 71.88246280 5.199377e+01 -147.2083 63.01667
#> 478 124.5000 M 0 NA 67.66391183 5.199866e+01 -147.2917 63.01667
#> 479 128.1500 M 0 NA 63.44498240 5.200902e+01 -147.3750 63.01667
#> 480 132.0625 M 0 NA 59.22606554 5.202484e+01 -147.4583 63.01667
#> 481 134.7500 L 0 NA 55.00755175 5.204614e+01 -147.5417 63.01667
#> 482 137.1250 L 0 NA 50.78867575 5.207290e+01 -147.6250 63.01667
#> 483 144.7000 L 0 NA 46.56982807 5.210513e+01 -147.7083 63.01667
#> 484 168.5000 L 0 NA 42.35139919 5.214283e+01 -147.7917 63.01667
#> 485 166.9375 L 0 NA 38.13262386 5.218599e+01 -147.8750 63.01667
#> 486 175.4375 L 0 NA 33.91389258 5.223463e+01 -147.9583 63.01667
#> 487 188.0000 L 0 NA 29.69559635 5.228873e+01 -148.0417 63.01667
#> 488 202.0500 L 1 0 25.47696842 5.234830e+01 -148.1250 63.01667
#> 489 220.2500 L 0 NA 21.25840080 5.241334e+01 -148.2083 63.01667
#> 490 238.8125 M 0 NA 17.04028345 5.248384e+01 -148.2917 63.01667
#> 491 263.6250 M 0 NA 12.82185118 5.255982e+01 -148.3750 63.01667
#> 492 291.0625 M 1 2 8.60349395 5.264127e+01 -148.4583 63.01667
#> 493 314.6000 M 1 0 4.38560374 5.272817e+01 -148.5417 63.01667
#> 494 336.7500 M 1 3 0.16741388 5.282056e+01 -148.6250 63.01667
#> 495 180.1250 L 0 NA 139.45534932 4.894582e+01 -145.8750 62.98333
#> 496 140.2857 L 1 2 135.23219588 4.886315e+01 -145.9583 62.98333
#> 497 122.0000 L 1 0 131.00935147 4.878596e+01 -146.0417 62.98333
#> 498 104.6667 M 1 11 126.78605003 4.871423e+01 -146.1250 62.98333
#> 499 148.1053 M 1 9 122.56268245 4.864798e+01 -146.2083 62.98333
#> 500 127.4375 M 1 6 118.33963967 4.858720e+01 -146.2917 62.98333
#> 501 119.0000 M 1 5 114.11615558 4.853189e+01 -146.3750 62.98333
#> 502 154.0000 M 1 0 109.89262109 4.848206e+01 -146.4583 62.98333
#> 503 113.8333 M 1 7 105.66942716 4.843770e+01 -146.5417 62.98333
#> 504 111.0000 M 1 19 101.44580764 4.839881e+01 -146.6250 62.98333
#> 505 112.6875 M 1 4 97.22215296 4.836540e+01 -146.7083 62.98333
#> 506 127.9375 M 1 4 92.99885559 4.833746e+01 -146.7917 62.98333
#> 507 111.6875 M 1 2 88.77514786 4.831499e+01 -146.8750 62.98333
#> 508 117.5000 L 0 NA 84.55142122 4.829799e+01 -146.9583 62.98333
#> 509 117.0833 L 0 NA 80.32806711 4.828646e+01 -147.0417 62.98333
#> 510 116.5833 L 0 NA 76.10431787 4.828041e+01 -147.1250 62.98333
#> 511 122.0833 L 0 NA 71.88056546 4.827983e+01 -147.2083 62.98333
#> 512 128.2500 L 1 0 67.65720182 4.828473e+01 -147.2917 62.98333
#> 513 129.8000 M 0 NA 63.43345929 4.829509e+01 -147.3750 62.98333
#> 514 132.8333 M 0 NA 59.20972932 4.831093e+01 -147.4583 62.98333
#> 515 136.0833 M 1 0 54.98640284 4.833224e+01 -147.5417 62.98333
#> 516 141.5000 L 0 NA 50.76271372 4.835903e+01 -147.6250 62.98333
#> 517 148.2667 L 0 NA 46.53905289 4.839129e+01 -147.7083 62.98333
#> 518 157.1667 L 0 NA 42.31581129 4.842901e+01 -147.7917 62.98333
#> 519 169.3333 L 0 NA 38.09222279 4.847222e+01 -147.8750 62.98333
#> 520 178.7500 L 0 NA 33.86867832 4.852089e+01 -147.9583 62.98333
#> 521 187.6667 L 0 NA 29.64556931 4.857504e+01 -148.0417 62.98333
#> 522 203.2667 L 0 NA 25.42212813 4.863466e+01 -148.1250 62.98333
#> 523 220.3333 L 0 NA 21.19874724 4.869976e+01 -148.2083 62.98333
#> 524 239.5000 L 0 NA 16.97581702 4.877032e+01 -148.2917 62.98333
#> 525 272.8333 L 0 NA 12.75257141 4.884636e+01 -148.3750 62.98333
#> 526 329.2500 M 0 NA 8.52940082 4.892787e+01 -148.4583 62.98333
#> 527 332.1500 M 1 3 4.30669764 4.901485e+01 -148.5417 62.98333
#> 528 347.5000 M 1 18 0.08369434 4.910732e+01 -148.6250 62.98333
#> 529 181.7368 L 0 NA 139.53043829 4.523247e+01 -145.8750 62.95000
#> 530 121.0625 L 1 0 135.30247293 4.514972e+01 -145.9583 62.95000
#> 531 115.3750 L 1 0 131.07481706 4.507246e+01 -146.0417 62.95000
#> 532 101.3750 M 1 9 126.84670376 4.500068e+01 -146.1250 62.95000
#> 533 103.9375 M 1 19 122.61852385 4.493437e+01 -146.2083 62.95000
#> 534 113.5833 M 1 2 118.39067021 4.487354e+01 -146.2917 62.95000
#> 535 118.9167 M 1 0 114.16237434 4.481819e+01 -146.3750 62.95000
#> 536 117.8000 M 1 11 109.93402811 4.476831e+01 -146.4583 62.95000
#> 537 134.6250 L 1 0 105.70602288 4.472392e+01 -146.5417 62.95000
#> 538 140.7500 L 1 0 101.47759165 4.468499e+01 -146.6250 62.95000
#> 539 118.5625 L 1 0 97.24912528 4.465155e+01 -146.7083 62.95000
#> 540 114.9375 L 1 0 93.02101666 4.462359e+01 -146.7917 62.95000
#> 541 115.5000 M 1 11 88.79249726 4.460110e+01 -146.8750 62.95000
#> 542 116.0500 L 0 NA 84.56395845 4.458408e+01 -146.9583 62.95000
#> 543 116.0000 L 0 NA 80.33579313 4.457255e+01 -147.0417 62.95000
#> 544 118.3125 L 0 NA 76.10723275 4.456649e+01 -147.1250 62.95000
#> 545 123.1250 L 0 NA 71.87866868 4.456591e+01 -147.2083 62.95000
#> 546 126.8125 L 0 NA 67.65049383 4.457081e+01 -147.2917 62.95000
#> 547 130.9500 L 0 NA 63.42193965 4.458119e+01 -147.3750 62.95000
#> 548 134.4375 L 0 NA 59.19339802 4.459704e+01 -147.4583 62.95000
#> 549 137.2500 L 0 NA 54.96526082 4.461837e+01 -147.5417 62.95000
#> 550 142.6875 M 1 0 50.73675951 4.464517e+01 -147.6250 62.95000
#> 551 150.4000 M 1 0 46.50828699 4.467746e+01 -147.7083 62.95000
#> 552 158.6250 M 1 0 42.28023413 4.471522e+01 -147.7917 62.95000
#> 553 168.9375 L 0 NA 38.05183389 4.475846e+01 -147.8750 62.95000
#> 554 180.6250 L 0 NA 33.82347768 4.480718e+01 -147.9583 62.95000
#> 555 189.8750 L 0 NA 29.59555683 4.486137e+01 -148.0417 62.95000
#> 556 208.9000 L 0 NA 25.36730436 4.492104e+01 -148.1250 62.95000
#> 557 226.6250 L 0 NA 21.13911114 4.498619e+01 -148.2083 62.95000
#> 558 244.8750 L 0 NA 16.91137002 4.505681e+01 -148.2917 62.95000
#> 559 282.8125 L 0 NA 12.68331252 4.513292e+01 -148.3750 62.95000
#> 560 319.7500 M 1 3 8.45533051 4.521450e+01 -148.4583 62.95000
#> 561 345.0000 M 0 NA 4.22781531 4.530155e+01 -148.5417 62.95000
#> 562 373.8750 L 0 NA 0.00000000 4.539409e+01 -148.6250 62.95000
#> 563 154.7368 L 0 NA 139.60550465 4.151912e+01 -145.8750 62.91667
#> 564 145.3125 L 1 9 135.37272880 4.143631e+01 -145.9583 62.91667
#> 565 139.6875 L 1 6 131.14026293 4.135899e+01 -146.0417 62.91667
#> 566 113.3125 M 1 18 126.90733921 4.128714e+01 -146.1250 62.91667
#> 567 105.3889 M 1 2 122.67434892 4.122077e+01 -146.2083 62.91667
#> 568 133.6111 M 1 0 118.44168537 4.115990e+01 -146.2917 62.91667
#> 569 142.1875 L 1 0 114.20857917 4.110450e+01 -146.3750 62.91667
#> 570 133.6923 L 1 6 109.97542264 4.105458e+01 -146.4583 62.91667
#> 571 146.2500 L 1 0 105.74260757 4.101014e+01 -146.5417 62.91667
#> 572 127.5333 L 1 0 101.50936608 4.097119e+01 -146.6250 62.91667
#> 573 120.0000 L 1 0 97.27608997 4.093772e+01 -146.7083 62.91667
#> 574 117.6875 L 1 0 93.04317106 4.090973e+01 -146.7917 62.91667
#> 575 117.1250 M 1 1 88.80984144 4.088722e+01 -146.8750 62.91667
#> 576 118.5294 L 0 NA 84.57649241 4.087020e+01 -146.9583 62.91667
#> 577 116.5789 L 0 NA 80.34351784 4.085865e+01 -147.0417 62.91667
#> 578 116.3125 M 1 0 76.11014674 4.085259e+01 -147.1250 62.91667
#> 579 121.4375 L 0 NA 71.87677299 4.085201e+01 -147.2083 62.91667
#> 580 125.6875 L 0 NA 67.64378787 4.085691e+01 -147.2917 62.91667
#> 581 133.0500 L 0 NA 63.41042348 4.086730e+01 -147.3750 62.91667
#> 582 141.3125 L 0 NA 59.17707164 4.088316e+01 -147.4583 62.91667
#> 583 148.8125 L 0 NA 54.94412416 4.090451e+01 -147.5417 62.91667
#> 584 150.5625 M 0 NA 50.71081313 4.093134e+01 -147.6250 62.91667
#> 585 157.1000 M 1 0 46.47753037 4.096365e+01 -147.7083 62.91667
#> 586 165.7500 M 1 2 42.24466768 4.100144e+01 -147.7917 62.91667
#> 587 173.5625 M 0 NA 38.01145718 4.104472e+01 -147.8750 62.91667
#> 588 182.8125 L 0 NA 33.77829015 4.109348e+01 -147.9583 62.91667
#> 589 195.4375 L 0 NA 29.54556044 4.114771e+01 -148.0417 62.91667
#> 590 214.5500 L 0 NA 25.31249712 4.120743e+01 -148.1250 62.91667
#> 591 231.8125 L 0 NA 21.07949403 4.127264e+01 -148.2083 62.91667
#> 592 253.4375 L 0 NA 16.84694243 4.134332e+01 -148.2917 62.91667
#> 593 288.5625 L 0 NA 12.61407450 4.141949e+01 -148.3750 62.91667
#> 594 194.0625 L 0 NA 143.91805145 3.789416e+01 -145.7917 62.88334
#> 595 212.0714 L 0 NA 139.68054833 3.780580e+01 -145.8750 62.88334
#> 596 224.5000 L 1 1 135.44296345 3.772291e+01 -145.9583 62.88334
#> 597 226.2857 M 1 5 131.20568902 3.764553e+01 -146.0417 62.88334
#> 598 192.1875 M 1 11 126.96795635 3.757362e+01 -146.1250 62.88334
#> 599 99.6250 L 1 3 122.73015712 3.750720e+01 -146.2083 62.88334
#> 600 129.9500 L 1 0 118.49268511 3.744627e+01 -146.2917 62.88334
#> 601 147.6250 L 0 NA 114.25477005 3.739082e+01 -146.3750 62.88334
#> 602 142.8125 L 0 NA 110.01680466 3.734086e+01 -146.4583 62.88334
#> 603 134.4375 L 0 NA 105.77918120 3.729639e+01 -146.5417 62.88334
#> 604 122.8000 L 0 NA 101.54113090 3.725740e+01 -146.6250 62.88334
#> 605 119.4667 L 0 NA 97.30304549 3.722390e+01 -146.7083 62.88334
#> 606 119.9167 L 0 NA 93.06531875 3.719589e+01 -146.7917 62.88334
#> 607 116.0000 M 1 3 88.82718037 3.717337e+01 -146.8750 62.88334
#> 608 121.5833 L 0 NA 84.58902258 3.715633e+01 -146.9583 62.88334
#> 609 119.6667 M 1 2 80.35123919 3.714477e+01 -147.0417 62.88334
#> 610 120.2500 M 1 0 76.11305986 3.713871e+01 -147.1250 62.88334
#> 611 122.5000 M 0 NA 71.87487685 3.713813e+01 -147.2083 62.88334
#> 612 124.7500 L 0 NA 67.63708393 3.714303e+01 -147.2917 62.88334
#> 613 135.2000 L 1 0 63.39891080 3.715342e+01 -147.3750 62.88334
#> 614 145.3750 L 0 NA 59.16075020 3.716930e+01 -147.4583 62.88334
#> 615 155.8125 L 0 NA 54.92299490 3.719067e+01 -147.5417 62.88334
#> 616 163.6250 L 0 NA 50.68487459 3.721752e+01 -147.6250 62.88334
#> 617 168.1500 M 1 0 46.44678304 3.724986e+01 -147.7083 62.88334
#> 618 177.1250 M 0 NA 42.20911199 3.728768e+01 -147.7917 62.88334
#> 619 186.3750 M 0 NA 37.97109266 3.733099e+01 -147.8750 62.88334
#> 620 195.2500 M 1 0 33.73311730 3.737979e+01 -147.9583 62.88334
#> 621 210.0625 L 0 NA 29.49557814 3.743407e+01 -148.0417 62.88334
#> 622 225.1500 L 0 NA 25.25770643 3.749385e+01 -148.1250 62.88334
#> 623 240.4375 L 0 NA 21.01989391 3.755911e+01 -148.2083 62.88334
#> 624 264.2143 L 0 NA 16.78253431 3.762985e+01 -148.2917 62.88334
#> 625 297.0833 L 0 NA 12.54485738 3.770608e+01 -148.3750 62.88334
#> 626 216.4375 L 0 NA 143.99788461 3.418072e+01 -145.7917 62.85000
#> 627 420.7500 L 0 NA 139.75557360 3.409227e+01 -145.8750 62.85000
#> 628 258.8000 M 1 8 135.51318035 3.400932e+01 -145.9583 62.85000
#> 629 120.8571 M 1 3 131.27109906 3.393187e+01 -146.0417 62.85000
#> 630 97.6667 M 1 25 127.02855860 3.385990e+01 -146.1250 62.85000
#> 631 106.6667 L 1 2 122.78595162 3.379343e+01 -146.2083 62.85000
#> 632 131.8947 L 1 13 118.54367233 3.373245e+01 -146.2917 62.85000
#> 633 142.7500 L 0 NA 114.30094957 3.367695e+01 -146.3750 62.85000
#> 634 145.6250 L 0 NA 110.05817652 3.362695e+01 -146.4583 62.85000
#> 635 142.3750 L 0 NA 105.81574585 3.358245e+01 -146.5417 62.85000
#> 636 129.8824 L 0 NA 101.57288792 3.354343e+01 -146.6250 62.85000
#> 637 120.5263 L 0 NA 97.32999541 3.350990e+01 -146.7083 62.85000
#> 638 120.2500 L 0 NA 93.08746100 3.348186e+01 -146.7917 62.85000
#> 639 115.8750 M 1 0 88.84451503 3.345932e+01 -146.8750 62.85000
#> 640 120.5625 M 1 0 84.60155019 3.344226e+01 -146.9583 62.85000
#> 641 122.2000 M 1 0 80.35895966 3.343070e+01 -147.0417 62.85000
#> 642 124.8750 M 0 NA 76.11597226 3.342463e+01 -147.1250 62.85000
#> 643 128.0000 M 0 NA 71.87298219 3.342405e+01 -147.2083 62.85000
#> 644 132.1667 M 0 NA 67.63038165 3.342896e+01 -147.2917 62.85000
#> 645 138.5333 L 0 NA 63.38740094 3.343936e+01 -147.3750 62.85000
#> 646 148.5833 L 0 NA 59.14443277 3.345525e+01 -147.4583 62.85000
#> 647 160.7500 L 0 NA 54.90186982 3.347663e+01 -147.5417 62.85000
#> 648 172.9167 L 0 NA 50.65894242 3.350351e+01 -147.6250 62.85000
#> 649 180.3333 M 0 NA 46.41604326 3.353587e+01 -147.7083 62.85000
#> 650 187.1667 M 0 NA 42.17356503 3.357373e+01 -147.7917 62.85000
#> 651 200.3333 M 1 40 37.93073805 3.361708e+01 -147.8750 62.85000
#> 652 209.1667 M 0 NA 33.68795503 3.366592e+01 -147.9583 62.85000
#> 653 224.7500 L 0 NA 29.44560862 3.372024e+01 -148.0417 62.85000
#> 654 239.8667 L 0 NA 25.20292920 3.378007e+01 -148.1250 62.85000
#> 655 259.3333 L 0 NA 20.96030893 3.384538e+01 -148.2083 62.85000
#> 656 223.2500 L 0 NA 144.07769359 3.046729e+01 -145.7917 62.81667
#> 657 250.7500 L 1 4 139.83057614 3.037877e+01 -145.8750 62.81667
#> 658 120.1579 M 1 0 135.58337700 3.029575e+01 -145.9583 62.81667
#> 659 97.9412 M 1 4 131.33648927 3.021823e+01 -146.0417 62.81667
#> 660 103.0625 M 1 4 127.08914249 3.014621e+01 -146.1250 62.81667
#> 661 114.6875 L 1 0 122.84172973 3.007967e+01 -146.2083 62.81667
#> 662 128.2308 M 0 NA 118.59464410 3.001864e+01 -146.2917 62.81667
#> 663 146.1333 M 0 NA 114.34711510 2.996310e+01 -146.3750 62.81667
#> 664 150.3333 L 0 NA 110.09953584 2.991306e+01 -146.4583 62.81667
#> 665 150.5714 L 1 0 105.85229942 2.986852e+01 -146.5417 62.81667
#> 666 137.2500 L 0 NA 101.60463532 2.982946e+01 -146.6250 62.81667
#> 667 127.0500 L 0 NA 97.35693614 2.979591e+01 -146.7083 62.81667
#> 668 124.0000 L 0 NA 93.10959655 2.976785e+01 -146.7917 62.81667
#> 669 119.5625 M 0 NA 88.86184445 2.974528e+01 -146.8750 62.81667
#> 670 121.7500 M 0 NA 84.61407348 2.972822e+01 -146.9583 62.81667
#> 671 127.0000 M 0 NA 80.36667729 2.971664e+01 -147.0417 62.81667
#> 672 131.3750 M 0 NA 76.11888377 2.971057e+01 -147.1250 62.81667
#> 673 135.0625 M 0 NA 71.87108709 2.970998e+01 -147.2083 62.81667
#> 674 134.9375 M 0 NA 67.62368139 2.971490e+01 -147.2917 62.81667
#> 675 144.8000 L 0 NA 63.37589457 2.972531e+01 -147.3750 62.81667
#> 676 153.7500 L 0 NA 59.12812028 2.974121e+01 -147.4583 62.81667
#> 677 165.5000 L 0 NA 54.88075165 2.976261e+01 -147.5417 62.81667
#> 678 181.1250 L 0 NA 50.63301811 2.978951e+01 -147.6250 62.81667
#> 679 192.9000 M 0 NA 46.38531281 2.982190e+01 -147.7083 62.81667
#> 680 199.1875 M 0 NA 42.13802884 2.985979e+01 -147.7917 62.81667
#> 681 208.6875 M 0 NA 37.89039568 2.990318e+01 -147.8750 62.81667
#> 682 227.1250 M 0 NA 33.64280645 2.995206e+01 -147.9583 62.81667
#> 683 244.7500 M 0 NA 29.39565476 3.000643e+01 -148.0417 62.81667
#> 684 262.8000 L 1 6 25.14816857 3.006630e+01 -148.1250 62.81667
#> 685 143.0000 L 0 NA 144.15747379 2.675409e+01 -145.7917 62.78333
#> 686 123.3333 L 1 0 139.90555163 2.666550e+01 -145.8750 62.78333
#> 687 99.3750 M 1 7 135.65354782 2.658241e+01 -145.9583 62.78333
#> 688 98.1000 M 1 9 131.40185590 2.650483e+01 -146.0417 62.78333
#> 689 135.1250 L 1 0 127.14970452 2.643274e+01 -146.1250 62.78333
#> 690 122.4375 L 0 NA 122.89748669 2.636615e+01 -146.2083 62.78333
#> 691 119.6875 M 1 3 118.64559748 2.630507e+01 -146.2917 62.78333
#> 692 141.7000 M 0 NA 114.39326398 2.624948e+01 -146.3750 62.78333
#> 693 150.4375 L 0 NA 110.14088023 2.619940e+01 -146.4583 62.78333
#> 694 146.2857 L 0 NA 105.88883980 2.615482e+01 -146.5417 62.78333
#> 695 135.2500 L 0 NA 101.63637126 2.611573e+01 -146.6250 62.78333
#> 696 136.6667 L 0 NA 97.38386767 2.608215e+01 -146.7083 62.78333
#> 697 129.4167 L 0 NA 93.13172410 2.605407e+01 -146.7917 62.78333
#> 698 124.2143 L 0 NA 88.87916761 2.603148e+01 -146.8750 62.78333
#> 699 125.3750 M 1 1 84.62659175 2.601440e+01 -146.9583 62.78333
#> 700 132.5000 M 0 NA 80.37439162 2.600282e+01 -147.0417 62.78333
#> 701 136.8750 M 1 0 76.12179424 2.599674e+01 -147.1250 62.78333
#> 702 146.3750 M 1 0 71.86919319 2.599615e+01 -147.2083 62.78333
#> 703 142.7500 M 0 NA 67.61698355 2.600107e+01 -147.2917 62.78333
#> 704 150.3000 L 0 NA 63.36439236 2.601149e+01 -147.3750 62.78333
#> 705 163.7500 L 0 NA 59.11181369 2.602741e+01 -147.4583 62.78333
#> 706 174.2500 L 0 NA 54.85964161 2.604883e+01 -147.5417 62.78333
#> 707 185.7500 L 0 NA 50.60710316 2.607575e+01 -147.6250 62.78333
#> 708 200.2500 M 0 NA 46.35459344 2.610817e+01 -147.7083 62.78333
#> 709 212.0625 M 1 2 42.10250548 2.614608e+01 -147.7917 62.78333
#> 710 220.6250 M 1 3 37.85006786 2.618951e+01 -147.8750 62.78333
#> 711 243.5625 M 1 10 33.59767416 2.623843e+01 -147.9583 62.78333
#> 712 152.1875 L 0 NA 144.23722978 2.304090e+01 -145.7917 62.75000
#> 713 131.0000 L 1 0 139.98050437 2.295224e+01 -145.8750 62.75000
#> 714 102.6667 M 1 7 135.72369735 2.286908e+01 -145.9583 62.75000
#> 715 99.2667 M 1 35 131.46720270 2.279143e+01 -146.0417 62.75000
#> 716 138.1429 L 1 0 127.21024818 2.271929e+01 -146.1250 62.75000
#> 717 138.9375 L 0 NA 122.95322775 2.265264e+01 -146.2083 62.75000
#> 718 139.1250 L 0 NA 118.69653539 2.259151e+01 -146.2917 62.75000
#> 719 131.2500 M 0 NA 114.43939885 2.253588e+01 -146.3750 62.75000
#> 720 151.1875 M 1 7 110.18221208 2.248575e+01 -146.4583 62.75000
#> 721 142.0625 M 0 NA 105.92536908 2.244114e+01 -146.5417 62.75000
#> 722 136.1250 L 1 0 101.66809757 2.240202e+01 -146.6250 62.75000
#> 723 144.5000 L 0 NA 97.41079101 2.236841e+01 -146.7083 62.75000
#> 724 135.2500 L 0 NA 93.15384494 2.234030e+01 -146.7917 62.75000
#> 725 129.5714 M 0 NA 88.89648551 2.231770e+01 -146.8750 62.75000
#> 726 130.0000 M 0 NA 84.63910724 2.230060e+01 -146.9583 62.75000
#> 727 138.2000 M 0 NA 80.38210462 2.228901e+01 -147.0417 62.75000
#> 728 142.1667 M 0 NA 76.12470382 2.228292e+01 -147.1250 62.75000
#> 729 154.0000 M 0 NA 71.86729985 2.228234e+01 -147.2083 62.75000
#> 730 153.4167 M 0 NA 67.61028774 2.228726e+01 -147.2917 62.75000
#> 731 160.5333 M 1 0 63.35289363 2.229769e+01 -147.3750 62.75000
#> 732 175.0833 L 0 NA 59.09551204 2.231362e+01 -147.4583 62.75000
#> 733 183.3571 L 0 NA 54.83853696 2.233506e+01 -147.5417 62.75000
#> 734 191.6250 L 0 NA 50.58119608 2.236200e+01 -147.6250 62.75000
#> 735 211.1500 L 1 29 46.32388339 2.239445e+01 -147.7083 62.75000
#> 736 138.8421 L 0 NA 144.31696150 1.932773e+01 -145.7917 62.71667
#> 737 113.9375 L 1 0 140.05543431 1.923900e+01 -145.8750 62.71667
#> 738 95.1250 M 1 20 135.79382552 1.915577e+01 -145.9583 62.71667
#> 739 186.0000 M 1 8 131.53252959 1.907806e+01 -146.0417 62.71667
#> 740 147.3750 L 1 3 127.27077341 1.900585e+01 -146.1250 62.71667
#> 741 147.0833 L 0 NA 123.00895081 1.893916e+01 -146.2083 62.71667
#> 742 155.7500 L 0 NA 118.74745779 1.887797e+01 -146.2917 62.71667
#> 743 136.6667 M 0 NA 114.48551967 1.882229e+01 -146.3750 62.71667
#> 744 147.1579 M 0 NA 110.22353133 1.877213e+01 -146.4583 62.71667
#> 745 145.8125 L 0 NA 105.96188724 1.872747e+01 -146.5417 62.71667
#> 746 142.3125 L 0 NA 101.69981422 1.868832e+01 -146.6250 62.71667
#> 747 141.4706 L 0 NA 97.43770615 1.865468e+01 -146.7083 62.71667
#> 748 141.6842 M 1 0 93.17595903 1.862655e+01 -146.7917 62.71667
#> 749 134.8125 M 1 0 88.91379814 1.860393e+01 -146.8750 62.71667
#> 750 134.3125 L 0 NA 84.65161789 1.858682e+01 -146.9583 62.71667
#> 751 143.2941 M 1 0 80.38981426 1.857522e+01 -147.0417 62.71667
#> 752 149.2105 M 0 NA 76.12761252 1.856913e+01 -147.1250 62.71667
#> 753 162.8125 M 1 0 71.86540710 1.856855e+01 -147.2083 62.71667
#> 754 164.6875 M 0 NA 67.60359398 1.857347e+01 -147.2917 62.71667
#> 755 170.0000 M 0 NA 63.34139841 1.858391e+01 -147.3750 62.71667
#> 756 184.4737 M 1 4 59.07921536 1.859985e+01 -147.4583 62.71667
#> 757 196.9286 M 0 NA 54.81743976 1.862131e+01 -147.5417 62.71667
#> 758 210.4167 L 0 NA 50.55529688 1.864827e+01 -147.6250 62.71667
#> 759 124.5294 L 0 NA 144.39666895 1.561458e+01 -145.7917 62.68333
#> 760 123.3125 L 0 NA 140.13034141 1.552577e+01 -145.8750 62.68333
#> 761 99.5625 M 0 NA 135.86393235 1.544248e+01 -145.9583 62.68333
#> 762 175.7500 M 0 NA 131.59783660 1.536470e+01 -146.0417 62.68333
#> 763 143.4000 L 0 NA 127.33128019 1.529244e+01 -146.1250 62.68333
#> 764 149.6875 L 0 NA 123.06465793 1.522568e+01 -146.2083 62.68333
#> 765 159.8750 L 0 NA 118.79836469 1.516445e+01 -146.2917 62.68333
#> 766 157.4286 L 0 NA 114.53162643 1.510873e+01 -146.3750 62.68333
#> 767 150.4667 M 1 0 110.26483800 1.505852e+01 -146.4583 62.68333
#> 768 157.8333 L 0 NA 105.99839427 1.501383e+01 -146.5417 62.68333
#> 769 153.0769 L 0 NA 101.73152119 1.497464e+01 -146.6250 62.68333
#> 770 148.4375 L 0 NA 97.46461309 1.494098e+01 -146.7083 62.68333
#> 771 147.2500 M 0 NA 93.19806639 1.491282e+01 -146.7917 62.68333
#> 772 142.1250 L 0 NA 88.93110549 1.489018e+01 -146.8750 62.68333
#> 773 138.6250 L 0 NA 84.66412575 1.487306e+01 -146.9583 62.68333
#> 774 148.1875 M 0 NA 80.39752257 1.486145e+01 -147.0417 62.68333
#> 775 158.0500 L 0 NA 76.13052033 1.485535e+01 -147.1250 62.68333
#> 776 176.8125 M 0 NA 71.86351492 1.485477e+01 -147.2083 62.68333
#> 777 180.8750 M 1 7 67.59690225 1.485970e+01 -147.2917 62.68333
#> 778 185.2500 M 1 3 63.32990670 1.487014e+01 -147.3750 62.68333
#> 779 203.0000 M 1 0 59.06292364 1.488610e+01 -147.4583 62.68333
#> 780 215.6875 M 1 3 54.79634796 1.490757e+01 -147.5417 62.68333
#> 781 229.4375 M 0 NA 50.52940558 1.493456e+01 -147.6250 62.68333
#> 782 152.0588 L 0 NA 144.47635663 1.190124e+01 -145.7917 62.65000
#> 783 134.9231 L 0 NA 140.20522995 1.181235e+01 -145.8750 62.65000
#> 784 103.0000 M 0 NA 135.93402127 1.172899e+01 -145.9583 62.65000
#> 785 108.2500 M 1 2 131.66312741 1.165115e+01 -146.0417 62.65000
#> 786 136.7000 L 0 NA 127.39177197 1.157883e+01 -146.1250 62.65000
#> 787 195.1250 L 0 NA 123.12035020 1.151202e+01 -146.2083 62.65000
#> 788 203.6875 L 1 0 118.84925895 1.145074e+01 -146.2917 62.65000
#> 789 159.6875 L 0 NA 114.57772176 1.139496e+01 -146.3750 62.65000
#> 790 153.5000 L 0 NA 110.30613442 1.134471e+01 -146.4583 62.65000
#> 791 168.1875 L 0 NA 106.03489225 1.129998e+01 -146.5417 62.65000
#> 792 161.2667 L 0 NA 101.76322030 1.126077e+01 -146.6250 62.65000
#> 793 155.0000 L 0 NA 97.49151387 1.122708e+01 -146.7083 62.65000
#> 794 152.5333 M 1 0 93.22016827 1.119890e+01 -146.7917 62.65000
#> 795 151.3333 L 0 NA 88.94840854 1.117624e+01 -146.8750 62.65000
#> 796 149.6667 L 0 NA 84.67663000 1.115910e+01 -146.9583 62.65000
#> 797 155.0000 M 1 0 80.40522845 1.114748e+01 -147.0417 62.65000
#> 798 169.3000 L 0 NA 76.13342741 1.114138e+01 -147.1250 62.65000
#> 799 190.0625 M 0 NA 71.86162373 1.114080e+01 -147.2083 62.65000
#> 800 199.8750 M 0 NA 67.59021218 1.114573e+01 -147.2917 62.65000
#> 801 203.0625 M 1 6 63.31841783 1.115618e+01 -147.3750 62.65000
#> 802 225.1500 M 1 2 59.04663597 1.117216e+01 -147.4583 62.65000
#> 803 170.1875 L 1 0 144.55601998 8.187910e+00 -145.7917 62.61666
#> 804 142.4000 L 1 8 140.28009561 8.098953e+00 -145.8750 62.61666
#> 805 165.9333 M 1 8 136.00408980 8.015521e+00 -145.9583 62.61666
#> 806 99.5000 M 0 NA 131.72839826 7.937618e+00 -146.0417 62.61666
#> 807 180.6667 L 0 NA 127.45224526 7.865232e+00 -146.1250 62.61666
#> 808 252.2778 L 0 NA 123.17602597 7.798370e+00 -146.2083 62.61666
#> 809 285.7500 M 0 NA 118.90013765 7.737036e+00 -146.2917 62.61666
#> 810 259.1875 L 0 NA 114.62380299 7.681220e+00 -146.3750 62.61666
#> 811 169.2105 M 0 NA 110.34741822 7.630928e+00 -146.4583 62.61666
#> 812 178.4706 L 0 NA 106.07137906 7.586162e+00 -146.5417 62.61666
#> 813 170.0000 L 0 NA 101.79490972 7.546916e+00 -146.6250 62.61666
#> 814 164.6250 M 0 NA 97.51840540 7.513193e+00 -146.7083 62.61666
#> 815 159.7000 L 0 NA 93.24226338 7.484995e+00 -146.7917 62.61666
#> 816 159.5000 L 0 NA 88.96570631 7.462318e+00 -146.8750 62.61666
#> 817 173.3750 L 0 NA 84.68912991 7.445165e+00 -146.9583 62.61666
#> 818 190.5714 L 0 NA 80.41293147 7.433535e+00 -147.0417 62.61666
#> 819 179.9333 M 0 NA 76.13633361 7.427427e+00 -147.1250 62.61666
#> 820 200.7500 L 0 NA 71.85973208 7.426843e+00 -147.2083 62.61666
#> 821 218.0000 M 0 NA 67.58352416 7.431781e+00 -147.2917 62.61666
#> 822 226.0000 M 1 31 63.30693248 7.442243e+00 -147.3750 62.61666
#> 823 154.4375 L 0 NA 144.63565441 4.474810e+00 -145.7917 62.58333
#> 824 198.7000 L 1 5 140.35493410 4.385780e+00 -145.8750 62.58333
#> 825 216.2500 L 0 NA 136.07413239 4.302279e+00 -145.9583 62.58333
#> 826 101.9375 M 0 NA 131.79364543 4.224313e+00 -146.0417 62.58333
#> 827 166.0000 M 1 3 127.51269660 4.151868e+00 -146.1250 62.58333
#> 828 270.2353 M 1 2 123.23168152 4.084951e+00 -146.2083 62.58333
#> 829 367.2500 M 0 NA 118.95099789 4.023567e+00 -146.2917 62.58333
#> 830 422.3333 L 0 NA 114.66986750 3.967705e+00 -146.3750 62.58333
#> 831 217.0714 L 0 NA 110.38868703 3.917371e+00 -146.4583 62.58333
#> 832 182.2000 L 0 NA 106.10785263 3.872569e+00 -146.5417 62.58333
#> 833 176.2500 L 0 NA 101.82658763 3.833290e+00 -146.6250 62.58333
#> 834 171.0625 M 0 NA 97.54528819 3.799540e+00 -146.7083 62.58333
#> 835 171.7500 L 1 0 93.26435047 3.771319e+00 -146.7917 62.58333
#> 836 214.8750 L 1 0 88.98299779 3.748624e+00 -146.8750 62.58333
#> 837 236.8750 L 0 NA 84.70162579 3.731456e+00 -146.9583 62.58333
#> 838 228.5625 L 0 NA 80.42063271 3.719817e+00 -147.0417 62.58333
#> 839 191.8500 L 0 NA 76.13923876 3.713704e+00 -147.1250 62.58333
#> 840 211.8125 L 0 NA 71.85784215 3.713119e+00 -147.2083 62.58333
#> 841 236.5625 L 0 NA 67.57683857 3.718062e+00 -147.2917 62.58333
#> 842 255.2500 L 1 9 63.29545130 3.728532e+00 -147.3750 62.58333
#> 843 252.1667 L 0 NA 144.71526444 7.617278e-01 -145.7917 62.55000
#> 844 256.8000 L 0 NA 140.42974964 6.726257e-01 -145.8750 62.55000
#> 845 129.6316 L 0 NA 136.14415350 5.890564e-01 -145.9583 62.55000
#> 846 128.0625 M 0 NA 131.85887259 5.110266e-01 -146.0417 62.55000
#> 847 128.3750 L 0 NA 127.57312940 4.385220e-01 -146.1250 62.55000
#> 848 216.6500 L 0 NA 123.28732000 3.715500e-01 -146.2083 62.55000
#> 849 310.3750 M 1 0 119.00184252 3.101159e-01 -146.2917 62.55000
#> 850 357.6250 M 1 6 114.71591788 2.542084e-01 -146.3750 62.55000
#> 851 235.3571 L 0 NA 110.42994317 2.038334e-01 -146.4583 62.55000
#> 852 191.2667 L 0 NA 106.14431501 1.589946e-01 -146.5417 62.55000
#> 853 185.5000 L 0 NA 101.85825582 1.196839e-01 -146.6250 62.55000
#> 854 181.0833 M 1 4 97.57216170 8.590565e-02 -146.7083 62.55000
#> 855 187.9333 L 0 NA 93.28643079 5.766205e-02 -146.7917 62.55000
#> 856 267.5500 L 0 NA 89.00028397 3.494797e-02 -146.8750 62.55000
#> 857 303.9375 L 0 NA 84.71411784 1.776622e-02 -146.9583 62.55000
#> 858 235.0000 M 1 0 80.42833056 6.117608e-03 -147.0417 62.55000
#> 859 209.5000 L 0 NA 76.14214301 0.000000e+00 -147.1250 62.55000Some of the variables of interest include
total, which has counts of moose (and isNAfor all sites that were not surveyed).strat, a covariate that is eitherLfor Low orMfor medium.surveyed, which is a0if the site wasn’t sampled and a1if the site was sampled.xandy, the spatial coordinates for the centroids of the sites (in a user-defined Trans-Mercator projection).
Fitting the Model and Obtaining Predictions
We can now proceed to use the functions in sptotal in a
similar way to how the functions were used for the simulated data. To
get a sense of the data, we first give a plot of the raw observed
counts:
ggplot(data = AKmoose_df, aes(x = x, y = y)) +
geom_point(aes(colour = total), size = 4) +
scale_colour_viridis_c() +
theme_bw()