text:
\section{Introduction}

Two networks composed of two different types of instruments are available in monitoring the PM$_{2.5}$ process in Taiwan.
Traditionally, PM$_{2.5}$ is monitored by large monitoring stations
in the Taiwan Air Quality Monitoring Network (TAQMN) of the Environmental Protection Administration (EPA).
These monitoring stations provide high-quality hourly measurements, but are costly to establish and operate.
Currently, TAQMN consists of $77$ stations (74 on the main island and 3 on the offshore islands),
which are deployed at heights of approximately 10 meters above the ground.
Recently, another network consisting of small, low-cost, internet-of-things microsensors, called AirBoxes, is established.
Although measurements from AirBoxes based on optical sensors are not as accurate as those from EPA monitoring stations,
they are broadly deployed (at around 3 meters height) and generate data about every 5 minutes, resulting in high spatial and temporal coverage.

Figures~\ref{fig:data}(a) and \ref{fig:data}(b) show the EPA data (in ppm from 74 stations on the main island)
and the AirBox data (in ppm from 1769 AirBoxes) at 9:00am on December 22, 2020.
Clearly, the AirBox network is considerably denser.
However, as seen in Figures~\ref{fig:data}(a) and \ref{fig:data}(b),
measurements from AirBoxes have higher variances and are usually higher than those from EPA stations.
These upward biases are partly caused by higher altitudes of EPA stations than AirBoxes,
as PM$_{2.5}$ concentrations tend to be lower at higher altitudes.
There are also some clear outlying measurements.
The goal of this article is to develop a reliable calibration method
so that calibrated PM$_{2.5}$ measurements from AirBoxes are consistent with those from EPA stations.

\begin{figure}[tb]\centering
\begin{tabular}{cc}
\includegraphics[scale=0.32,trim={0cm 0cm 0cm 0cm},clip]{EPA_2020-12-22_09.png}
&  \includegraphics[scale=0.32,trim={0cm 0cm 0cm 0cm},clip]{Airbox_2020-12-22_09.png}\\

(a) & (b)
\end{tabular}
\caption{PM$_{2.5}$ measurements at 9:00am on December 22, 2020: (a) from 74 EPA stations;
(b) from 1769 AirBoxes.}
\label{fig:data}
\end{figure}

One effective way to calibrate AirBoxes is by regression, which works well for AirBoxes colocated at (or very close to) EPA stations.
The method is particularly effective if it suffices to apply a universal calibration line to all AirBoxes.
However, as shown in the next section, different calibrations are needed for AirBoxes located at various locations
with different local environments.
Additionally, most AirBoxes are away from EPA stations and cannot be calibrated directly, challenging the calibration task.
We propose to explore the relationship in the two datasets
and leverage the proximity of nearby AirBoxes and EPA stations using a spatially varying-coefficients model.

The rest of this paper is organized as follows. Section 2 compares PM$_{2.5}$ data between the two networks.
In Section 3, we introduce our proposed calibration method.
We also provide a robust parameter estimation procedure and a spatial prediction method that incorporates the two types of measurements.
The calibration results are given in Section 4. Finally, Section 5 provides a brief summary.

\section{Comparisons between EPA and AirBox Data}

We compare EPA and AirBox data observed in December, 2020 to give some ideas about how they differ.
The data being analyzed in this paper are available at Civil IoT Taiwan Data Service Platform.
The EPA TAQMN data can be downloaded from \url{https://ci.taiwan.gov.tw/dsp/en/environmental_air_epa_en.aspx},
and the AirBox data can be downloaded from \url{https://ci.taiwan.gov.tw/dsp/history/iis_airbox/}.

Since TAQMN produces hourly data,
we first aggregate the raw AirBox data into hourly data by averaging over all data for each hour and each site.
Thus, we obtain $\bm{z}_t=(z_t(\bm{s}_1),\dots,z_t(\bm{s}_n))'$ at locations $\bm{s}_1,\dots,\bm{s}_n\in D$ and hour $t$ with possible missing values,
where $n=$2640, $t=1,\dots,T$, and $D\in\mathbb{R}^2$ is a region containing the main island of Taiwan.
As a preliminary data analysis, we choose data at $T=666$ hours, which have at least 500 non-missing observations in each $\bm{z}_t$; $t=1,\dots,T$.
We denote the corresponding EPA data at hour $t$ by $\bm{z}^*_t=(z^*_t(\bm{s}^*_1),\dots,z^*_t(\bm{s}^*_m))'$; $t=1,\dots,T$,
where $\bm{s}^*_1,\dots,\bm{s}^*_m\in D$ and $m=74$.

It is known that AirBox data tend to have high variation,
and produce slightly higher PM$_{2.5}$ measurements than the corresponding EPA measurements.
This upward bias can be seen in Figures~\ref{fig:data}(a) and \ref{fig:data}(b),
and is partly caused by lower altitudes of AirBoxes (mostly deployed at around 3 meters) than EPA
equipments (placed at around 10 meters).
To examine the data more closely from the two different networks, we find 12 EPA stations that have at least 5 AirBoxes within their 2 km range.
Specifically, let $\bm{s}^*_j$ be the location of such an EPA station, then for $N^*_j\equiv\{i:\|\bm{s}_i-\bm{s}^*_j\|\leq 2\}$, we have $|N^*_j|\geq 5$.
Let $\bm{s}_{j'}\in N^*_j$ be the AirBox location nearest to $\bm{s}^*_j$. That is, $j'\equiv\mathop{\arg\min}_{i\in N^*_j}\|\bm{s}_i-\bm{s}^*_j\|$.
Figure~\ref{fig:nearest} shows scatter plots $\big\{\big(z^*_t(\bm{s}^*_{j}),z_t(\bm{s}_{j'})\big):t=1,\dots,T\big\}$ of hourly PM$_{2.5}$ (in ppm)
between the two subsets of data at the 12 EPA stations.
Although $\big\{z^*_t(\bm{s}^*_j):t=1,\dots,T\big\}$ and $\big\{z_t(\bm{s}_{j'}):t=1,\dots,T\big\}$ are positively correlated,
their coefficient-of-determination ($R^2$) values ranging only from $0.32$ to $0.83$.
The discrepancies between AirBox and EPA data have made AirBoxes a significant concern regarding their measuring accuracy.

Nevertheless, it is possible to reduce the variance by utilizing many closely located AirBoxes.
We take a simple average over the AirBox measurements falling within 2 km radius of an EPA station at each hour $t$.
Substituting these for the corresponding AirBox measurements in Figure~\ref{fig:nearest}, we obtain Figure~\ref{fig:ave}
with each plot showing points $\big\{\big(z^*_t(\bm{s}^*_{j}),\bar{z}_t(\bm{s}^*_j)\big):t=1,\dots,T\big\}$ corresponding to an EPA station at $\bm{s}^*_j$,
where $\bar{z}_t(\bm{s}^*_j)\equiv\displaystyle\frac{1}{|N^*_j|}\sum_{i\in N^*_j}z_t(\bm{s}_i)$.
Comparing Figure~\ref{fig:ave} with Figure~\ref{fig:nearest},
the averaged PM$_{2.5}$ values from AirBoxes can be seen to match the EPA measurements much better with larger $R^2$ values.
Indeed, unity is strength; even though one AirBox is not very useful, many together can average out noise.
However, the intercepts and the slopes of the fitted regression lines appear to vary from sites to sites
with no common pattern, showing the need of site dependent calibrations.

\begin{figure}[tbh]\centering
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox23.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox31.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox26.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox32.png}\\
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox28.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox69.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox40.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox51.png}\\
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox59.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox65.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox64.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{NearestAirbox67.png}
\caption{Scatter plots of hourly PM$_{2.5}$ concentrations (in ppm) for twelve EPA stations
(in the $x$ axis with their locations shown in Figure \ref{fig:lsfit}) and
their nearest AirBoxes (in the $y$ axis) based on data in December, 2020,
where the blue dash line is the 45-degree line and the red solid line is the fitted regression line in each plot.}
\label{fig:nearest}
\end{figure}

\begin{figure}[tbh]\centering
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox23.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox31.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox26.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox32.png}\\
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox28.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox69.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox40.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox51.png}\\
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox59.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox65.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox64.png}
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{aveNearestAirbox67.png}
\caption{Scatter plots of hourly PM$_{2.5}$ concentrations (in ppm) for twelve EPA stations
(in the $x$ axis with their locations shown in Figure \ref{fig:lsfit}) and
the average PM$_{2.5}$ values (in ppm) over the corresponding AirBoxes within 2 km radius (in the $y$ axis)
based on data in December, 2020, where the blue dash line is the 45-degree line and the red solid line is the fitted regression line in each plot.}
\label{fig:ave}
\end{figure}

To visualize how these regression lines vary in space,
we first perform ordinary kriging to obtain a PM$_{2.5}$ predicted surface
for each $t=1,\dots,T$ based on AirBox data $\bm{z}_t$
using the isotropic exponential covariance model with the nugget effect,
where the parameters are estimated by maximum likelihood.
Let $\{\tilde{z}^{(\mathrm{ok})}_t(\bm{s}):\bm{s}\in D\}$ be the ordinary-kriging surface, for $t=1,\dots,T$.
Then for each $j=1,\dots,74$, we regress $\tilde{z}^{(\mathrm{ok})}_t(\bm{s}^*_j)$ on $z^*_t(\bm{s}^*_j)$ based on
$\big\{\big(z^*_t(\bm{s}^*_j),\tilde{z}^{(\mathrm{ok})}_t(\bm{s}^*_j)\big):t=1,\dots,T\big\}$ and obtain 74 calibrated regression lines
corresponding to 74 EPA stations in the main island Taiwan.
The resulting intercepts and slopes are illustrated as maps in Figure~\ref{fig:lsfit}.
Surprisingly, both the intercepts and the slopes exhibit spatial patterns.
For example, the intercepts are smoothly varying and mainly positive, with larger values in the south than in the north.
In contrast, the slopes are mostly less than one in the south but greater than one in the north.
These patterns are likely caused by similar chemical compositions of PM$_{2.5}$ at nearby locations,
which motivates us to develop a statistical model accounting for the patterns.

\begin{figure}[tbh]\centering
\begin{tabular}{cc}
  \includegraphics[scale=0.32,trim={0cm 0cm 0cm 0cm},clip]{Intercept_OK.png}
&  \includegraphics[scale=0.32,trim={0cm 0cm 0cm 0cm},clip]{Slope_OK.png}\\
(a) & (b)
\end{tabular}
\caption{Maps of (a) intercepts and (b) slopes of the preliminary calibrated regression lines obtained
by regressing kriged AirBox predicted values on the corresponding EPA data.}
\label{fig:lsfit}
\end{figure}

\section{The Proposed Method}

\subsection{The calibration model}
\label{sec:model}

Let $\{y^*_t(\bm{s}):\bm{s}\in D\}$ be the underlying PM$_{2.5}$ process at time $t$, which is assumed to be a Gaussian spatial process.
We observe two types of data, which are given by the following measurement equations, for $t=1,\dots,T$:
\begin{align}
   z_t(\bm{s}_i)
=&~ y_t(\bm{s}_i)+\varepsilon_t(\bm{s}_i);\quad i=1,\dots,n,
\label{eq:data1}\\
  z^*_t(\bm{s}^*_j)
=&~ y^*_t(\bm{s}^*_j)+\xi_t(\bm{s}^*_j);\quad j=1,\dots,m,
\label{eq:data2}
\end{align}

\noindent where $\{y_t(\bm{s}):\bm{s}\in D\}$ is a hidden Gaussian process,
$\varepsilon_t(\bm{s}_i)\sim N(0,\sigma_{\varepsilon t}^2(\bm{s}_i))$; $i=1,\dots,n$,
and $\xi_t(\bm{s}^*_j)\sim N(0,\sigma_{\xi t}^2)$; $j=1,\dots,m$.
Here $\{\varepsilon_t(\bm{s}_i)\}$ and $\{\xi_t(\bm{s}^*_j)\}$ are mutually uncorrelated.
Our goal is to find a calibration formula for $z_t(\cdot)$
so that after calibration it is close to $y^*_t(\cdot)$ as much as possible, for $t=1,\dots,T$.

Since we expect $\sigma_{\xi t}^2$ to be very small, we assume it to be zero in our data analysis.
That is, $z^*_t(\bm{s}^*_j)$ measures PM$_{2.5}$ precisely with $z^*_t(\bm{s}^*_j)=y^*_t(\bm{s}^*_j)$,
for $j=1,\dots,m$ and $t=1,\dots,T$.
On the other hand,  $\sigma_{\varepsilon t}^2(\bm{s}_i)$ tends to increase with $y_t(\bm{s}_i)$.
We model it as a piecewise linear function of $y(\bm{s}_i)$ with two pieces (having slopes $a_1$ and $a_2$) connected at $a_3$:
\begin{equation}
\sigma^2_{\varepsilon t}(\bm{s}_i)=a_0+a_1\, y_t(\bm{s}_i)+(a_2-a_1)(y_t(\bm{s}_i)-a_3)_+;\quad i=1,\dots,n,\,t=1,\dots,T,
\label{eq:sigmasq}
\end{equation}

\noindent where $\bm{a}=(a_0,a_1,a_2,a_3)'\in[0,\infty)^4$ consists of unknown parameters and $c_+\equiv\max(c, 0)$.

Motivated by the preliminary calibration results at EPA locations demonstrated on Figure~\ref{fig:lsfit},
we propose the following calibration equation, which links $y(\bm{s})$ to the true PM$_{2.5}$ process $y^*(\bm{s})$:
\begin{align}
y^*(\bm{s}) =&~ f_0(\bm{s})+f_1(\bm{s})y(\bm{s});\quad\bm{s}\in D,
\label{eq:calibration}
\end{align}

\noindent where $f_0(\cdot)$ is an unknown function of the intercept and $f_1(\cdot)$ is an unknown function of the slope.
Following Huang \textit{et al}.~(2018), we model the hidden Gaussian process $y_t(\cdot)$ corresponding to AirBoxes as:
\begin{align}
  y_t(\bm{s})
=&~\bm{\varphi}(\bm{s})'\bm{\alpha}_t+\bm{x}_t(\bm{s})'\bm{\beta}_t+\eta_t(\bm{s})\notag\\
=&~ \sum_{k=1}^{K}\alpha_k\varphi_k(\bm{s})+\sum_{\ell=1}^p\beta_{t\ell}x_{t\ell}(\bm{s})+\eta_t(\bm{s});\quad \bm{s}\in D,\,t=1,\dots,T,
\label{eq:model}
\end{align}

\noindent where $\mathrm{E}(y_t(\bm{s}))=\bm{\varphi}(\bm{s})'\bm{\alpha}_t+\bm{x}_t(\bm{s})'\bm{\beta}_t$ captures the large-scale features in terms of regressors,
$\bm{\varphi}(\bm{s})=(\varphi_1(\bm{s}),\dots,\varphi_{K}(\bm{s}))'$ are the first $K$ multi-resolution spline basis functions
with respect to the control points $\{\bm{s}_1,\dots,\bm{s}_n\}$
proposed by Tzeng and Huang (2018),
$\bm{x}_t(\bm{s})=(x_{t1}(\bm{s}),\dots,x_{tp}(\bm{s}))'$ consists of $p$ covariates,
$(\bm{\alpha}'_t,\bm{\beta}'_t)'\in\mathbb{R}^{K+p}$ are regression coefficients,
and $\eta_t(\cdot)$ is a zero-mean spatial dependent process parametrized by the isotropic exponential covariance model:
\[
C_t(\bm{s}-\bm{u})\equiv\mathrm{cov}(\eta_t(\bm{s}),\eta_t(\bm{u}))=v^2_t\exp(-\|\bm{s}-\bm{u}\|/\lambda_t);\quad\bm{s},\bm{u}\in D,\,t=1,\dots,T,
\]
with $\{v^2_t\}$ and $\{\lambda_t\}$ being the variance and the range parameters.

\subsection{Parameter estimation}
\label{sec:estimation}

We assume that $\sigma_{\xi t}^2$ is known, and zero in the data analysis.
Hence the functions and parameters need to be estimated are given by
$f_0(\cdot)$, $f_1(\cdot)$, $\bm{\theta}_t\equiv(\bm{\alpha}'_t,\bm{\beta}'_t,v^2_t,\lambda_t)'$; $t=1,\dots,T$, and $\bm{a}$.
For $t=1,\dots,T$, let $\bm{\Phi}_t$ be an $n\times K$ matrix with the $(i,k)$-th entry $\varphi_k(\bm{s}_i)$,
and $\bm{X}_t$ be an $n\times p$ matrix with the $(i,\ell)$-th entry $x_{t \ell}(\bm{s}_i)$.
Then from \eqref{eq:data1} and \eqref{eq:model},
the AirBox observations can be rewritten as:
\begin{equation}
\bm{z}_t=\bm{\Phi}_t\bm{\alpha}_t+\bm{X}_t\bm{\beta}_t+\bm{\eta}_t+\bm{\varepsilon}_t;\quad t=1,\dots,T,
\label{eq:data3}
\end{equation}

\noindent where $\bm{\eta}_t\equiv(\eta_t(\bm{s}_1),\dots,\eta_t(\bm{s}_n))'$ and
$\bm{\varepsilon}_t\equiv(\varepsilon_t(\bm{s}_1),\dots,\varepsilon_t(\bm{s}_n))'$.
This, together with \eqref{eq:data2}-\eqref{eq:model},
gives a complete picture of our model.

The model containing many parameters is flexible and can capture spatial heterogeneities.
How to estimate them are illustrated in the following three sub-sections.
How to select $K$ (i.e., the number of basis functions) is discussed in Section~\ref{sec:selection}.
Since there isn't much gain in statistical efficiency to consider a full likelihood approach when data are plenty,
and it is essential to account for outliers,
we estimate the parameters in steps using several robust methods.
For ease of notation, we provide detailed formulae only for fully observed data.

\subsubsection{Estimation of regression parameters $\{\bm{\alpha}_t\}$ and $\{\bm{\beta}_t\}$}
\label{sec:estimation1}

From \eqref{eq:data3},
for each $t=1,\dots,T$, we estimate $\bm{\alpha}_t$ and $\bm{\beta}_t$  using Huber's M-estimator (Huber and Ronchetti, 2009):
\[
\big(\hat{\bm{\alpha}}_t,\hat{\bm{\beta}}_t\big)=\mathop{\arg\min}_{(\bm{\alpha},\bm{\beta})}\sum_{i=1}^n
\rho\big(\delta_t(\bm{s}_i)\big/\sigma_{\delta t}\big);\quad t=1,\dots,T,
\]
where $\delta_t(\bm{s}_i)\equiv z_t(\bm{s}_i)-\bm{\varphi}(\bm{s}_i)'\bm{\alpha}-\bm{x}_t(\bm{s}_i)'\bm{\beta}$,
\[
\sigma_{\delta t}\equiv\mathrm{MAD}\big(\delta_t(\bm{s}_1),\dots,\delta_t(\bm{s}_n)\big)
\equiv\frac{1}{\Psi^{-1}(0.75)}\mathrm{median}\big(\big|\{\delta_t(\bm{s}_i)\}-\mathrm{median}(\{\delta_t(\bm{s}_i)\})\big|\big)
\]
is a robust estimate of the standard deviation of $\delta_t(\bm{s}_i)$ based on the median absolute deviation (MAD),
$\Psi(\cdot)$ is the cumulative distribution function of the standard normal distribution, and
\[
\rho(x)=\left\{
\begin{array}{ll}
\displaystyle\frac{1}{2}x^2; & \mbox{if }|x|\leq c,\\
c|x|-\displaystyle\frac{1}{2}c^2; & \mbox{if }|x|>c,
\end{array}
\right.
\]
is Huber's function. Here $c=1.345$ is commonly chosen, which gives an efficiency of 95\% if the regression errors are normally distributed.
The resulting residuals are given by
\begin{equation}
\hat{\bm{\delta}}_t\equiv\big(\hat{\delta}_t(\bm{s}_1),\dots,\hat{\delta}_t(\bm{s}_n)\big)'=
\bm{z}_t-\bm{\Phi}'_t\hat{\bm{\alpha}}_t-\bm{X}_t\hat{\bm{\beta}}_t;\quad t=1,\dots,T.
\label{eq:delta}
\end{equation}

\noindent In our data analysis, we consider no covariates $\bm{X}_t$ and select $K=25$ basis functions determined by the locations of the AirBox data at time $t$ to obtain $\bm{\Phi}_t$.

\subsubsection{Estimation of spatial covariance parameters $\{v_t^2\}$ and $\{\lambda_t\}$}
\label{sec:estimation2}

Since from \eqref{eq:sigmasq}, $\{\sigma_{\varepsilon t}^2(\bm{s}_i)\}$ are heterogeneous in space,
the conventional variogram approach cannot be applied directly to estimate $v_t$ and $\lambda_t$.
Instead, for each $t=1,\dots,T$, we propose to estimate $v^2_t$ and $\lambda_t$, by fitting the covariances:
\[
\tau_{ht}\equiv v^2_t\exp(-h/\lambda_t);\quad h\in\mathcal{H},
\]
based on a highly robust minimum covariance determinant estimator $\hat{\tau}_{ht}$ of Rousseeuw and van Driessen (1999)
at $h\in\mathcal{H}$ with $\mathcal{H}$ a pre-specified set of distances.
Specifically, for $t=1,\dots,T$ and $h\in\mathcal{H}$, we obtain $\hat{\tau}_{ht}$ based on $\{\big(\hat{\delta}_t(\bm{s}_i),\hat{\delta}_t(\bm{s}_k)\big):(i,k)\in\mathcal{T}_h\}$ with
$\mathcal{T}_h\equiv\{(i,k):h-\Delta<\|\bm{s}_i-\bm{s}_k\|\leq h+\Delta\}$ a tolerance region consisting of pairs distanced between $h+\Delta$ and $h+\Delta$.
After $\{\hat{\tau}_{ht}\}$ are obtained,
we estimate $v^2_t$ and $\lambda_t$ by the constrained least-squares estimators:
\[
\big(\hat{v}^2_t,\hat{\lambda}_t\big)'\equiv\mathop{\arg\min}_{(v^2,\lambda)'\in(0,\infty)^2}\sum_{h\in\mathcal{H}}
\{\hat{\tau}_{ht}-v^2\exp(-h/\lambda)\}^2;\quad t=1,\dots,T.
\]
In our data analysis, we select $\mathcal{H}=\{1/2,2/2,\dots,49/2\}$ (in km) and $\Delta=1/2$ (in km).

\subsubsection{Estimation of measurement-error variance parameters $\bm{a}$}
\label{sec:estimation3}

From \eqref{eq:sigmasq}, we estimate the heterogeneous measurement-error variances
by utilizing a particular subset of the AirBox data in 2020.
This dataset contains 25 AirBoxes at a common location $\bm{s}_0$ (with longitude $121.451^{\circ}$ E and latitude $25.062^{\circ}$ N),
enabling us to focus on measurement-error variances with no other confounding factors.
As before, we aggregate the AirBox data into hourly data.
Because the data are colocated at $\bm{s}_0$,
it is reasonable to assume that the discrepancies between AirBox measurements are fully contributed by measurement errors.

We first check the consistency of measurements from these 25 AirBoxes by computing their mutual sample correlation coefficients.
We remove observations from 13 AirBoxes, two of which have no records and eleven of which have sample correlations with the others all smaller than $0.85$.
For $t=1,\dots,T$, let $\{w_{tj}:j\in\mathcal{J}_t\}$ be the observations available from the remaining 12 AirBoxes,
where $\mathcal{J}_t$ is the corresponding index set.
Then a robust estimate of $\sigma_{\varepsilon t}(\bm{s}_0)$ in \eqref{eq:sigmasq} is given by
$\tilde{\sigma}_{\varepsilon t}\equiv\mathrm{MAD}\big(\big\{w_{tj}:j\in\mathcal{J}_t \big\}\big)$, for $t=1,\dots,T$.

Let $\tilde{z}_{t}$ be the $10\%$ trimmed mean of $\{w_{tj}:j\in\mathcal{J}_t\}$.
We then estimate $\bm{a}\equiv(a_0,a_1,a_2,a_3)'$ in \eqref{eq:sigmasq} by regressing $\{\tilde{\sigma}^2_{\varepsilon t}\}$ on $\{\tilde{z}_{t}\}$ using the following constrained least-squares estimator:
\begin{align}
\hat{\bm{a}}\equiv(\hat{a}_{0},\hat{a}_{1},\hat{a}_{2},\hat{a}_{3})'=\mathop{\arg\min}_{\bm{a}\in[0,\infty)^4}\sum_{t=1}^{T}
\big\{\tilde{\sigma}_{\varepsilon t }^2-a_0-a_1\tilde{z}_{t}-(a_2-a_1)(\tilde{z}_{t}-a_3)_{+}\big\}^2.
\label{eq:a0a1}
\end{align}

\noindent Finally, the proposed estimator of $\sigma^2_{\varepsilon t}(\bm{s}_i)$ is given by
\[
\hat{\sigma}^2_{\varepsilon t}(\bm{s}_i)=\hat{a}_{0}+\hat{a}_{1}z_t(\bm{s}_i)
+(\hat{a}_2-\hat{a}_1)(\tilde{z}_{t}-\hat{a}_3)_{+};\quad i=1,\dots,n,\,t=1,\dots, T.
\]
The estimator is guaranteed to be monotonically non-decreasing in $\tilde{z}_t$ with a slope change at $\hat{a}_3$.
Figure \ref{fig:me} shows the scatter plot of $\{\tilde{\sigma}_{\varepsilon t}^2\}$ versus $\{\tilde{z}_{t}\}$
and the fitted piecewise linear regression line based on the data observed in 2020,
where $\hat{a}_0=0$ and the two slopes are $\hat{a}_1=0.54$ and $\hat{a}_2=7.13$ with the slope change at $\hat{a}_3=2.64$.

\begin{figure}\centering
\includegraphics[scale=1,trim={0cm 0cm 0cm 0cm},clip]{me3.png}
\caption{The scatter plot of $\{\tilde{\sigma}_{\varepsilon t j}^2\}$ versus $\{\tilde{z}_{tj}\}$ based on the data observed in the year 2020,
where the solid line is the fitted piecewise-linear regression line given in \eqref{eq:a0a1}.}
\label{fig:me}
\end{figure}

\subsubsection{Estimation of $f_0(\cdot)$ and $f_1(\cdot)$}
\label{sec:estimation4}

We develop a three-step procedure to estimate $f_0(\cdot)$ and $f_1(\cdot)$
by first obtaining predictors of $\{y_t(\bm{s}^*_j):j=1,\dots,m,\,t=1,\dots,T\}$,
followed by estimating $f_0(\bm{s}^*_j)$ and $f_1(\bm{s}^*_j)$ for $j=1,\dots,m$,
and then applying a kriging method to estimate $f_0(\cdot)$ and $f_1(\cdot)$.

First, for $t=1,\dots,T$, the empirical best linear predictor of $y_t(\bm{s})$ based on $\bm{z}_t$ with the estimated parameters,
$\hat{\bm{a}}$, $\hat{\bm{\alpha}}_t$, $\hat{\bm{\beta}}_t$,  $\hat{v}^2_t$ and $\hat{\lambda}_t$ plugged-in, is given by
\begin{equation}
\tilde{y}_t(\bm{s})=\bm{\varphi}(\bm{s})'\hat{\bm{\alpha}}_t+\bm{x}(\bm{s})'\hat{\bm{\beta}}_t
+\hat{\bm{c}}_t(\bm{s})\big(\hat{\bm{\Sigma}}_{\eta t}+\hat{\bm{\Sigma}}_{\varepsilon t}\big)^{-1}(\bm{z}_t-\bm{\Phi}_t\hat{\bm{\alpha}}_t-\bm{X}_t\hat{\bm{\beta}}_t),
\label{eq:uk}
\end{equation}

\noindent where
$\hat{\bm{c}}_t(\bm{s})\equiv\big(\hat{v}^2_t
\exp\big(-\|\bm{s}-\bm{s}_1\|/\hat{\lambda}_t\big),\dots,\hat{v}^2_t\exp\big(-\|\bm{s}-\bm{s}_n\|/\hat{\lambda}_t\big)\big)'$
is an estimator of
$\bm{c}_t(\bm{s})\equiv\big(v^2_t\exp\big(-\|\bm{s}-\bm{s}_1\|/\lambda_t\big),\dots,v^2_t\exp\big(-\|\bm{s}-\bm{s}_n\|/\lambda_t\big)\big)'$,
$\hat{\bm{\Sigma}}_{\eta t}$ is an $n\times n$ matrix with the $(i,j)$-th entry $\hat{v}^2_t\exp\big(-\|\bm{s}_i-\bm{s}_j\|/\hat{\lambda}_t\big)$, and
$\hat{\bm{\Sigma}}_{\varepsilon t}\equiv\mathrm{diag}\big(\hat{\sigma}_{\varepsilon t}^2(\bm{s}_1),\dots,\hat{\sigma}_{\varepsilon t}^2(\bm{s}_n)\big)$.

Next, we estimate $f_0(\bm{s}^*_j)$ and $f_1(\bm{s}^*_j)$ in \eqref{eq:calibration}, for $j=1,\dots,m$,
by applying a regression calibration method.
If it is reasonable to assume that both $f_0(\cdot)$ and $f_1(\cdot)$ are constant functions,
then it suffices to consider a global calibration line by simply regressing $\{z^*_t(\bm{s}^*_j):j=1,\dots,m,\,t=1,\dots,T\}$ on $\big\{\tilde{y}_t(\bm{s}^*_j):j=1,\dots,m,\,t=1,\dots,T\big\}$,
leading to the ordinary-least-squares (OLS) estimators for the two constant functions of $f_0(\cdot)$ and $f_1(\cdot)$:
\begin{equation}
  \tilde{f}^{(g)}_0
= \bar{z}-\tilde{f}^{(g)}_1\bar{y},\quad
  \tilde{f}^{(g)}_1
= \frac{\sum_{t=1}^T\sum_{j=1}^m\big(\tilde{y}_t(\bm{s}^*_j)-\bar{y}\big)\big(z^*_t(\bm{s}^*_j)-\bar{z}\big)}{\sum_{t=1}^T\sum_{j=1}^m\big(\tilde{y}_t(\bm{s}^*_j)-\bar{y}\big)^2},
\label{eq:OLS}
\end{equation}

\noindent where $\bar{y}\equiv\sum_{t=1}^T\sum_{j=1}^m \tilde{y}_t(\bm{s}^*_j)/(mT)$ and $\bar{z}\equiv\sum_{t=1}^T\sum_{j=1}^m z^*_t(\bm{s}^*_j)/(mT)$.

To achieve spatially adaptive calibration,
we first regress $\{z^*_t(\bm{s}^*_j):t=1,\dots,T\}$ on $\big\{\tilde{y}_t(\bm{s}^*_j):t=1,\dots,T\big\}$,
and obtain preliminary estimators $\tilde{f}_0(\bm{s}^*_j)$ and $\tilde{f}_1(\bm{s}^*_j)$ of $f_0(\bm{s}^*_j)$ and $f_1(\bm{s}^*_j)$
at the data locations $\{\bm{s}^*_j:j=1,\dots,m\}$ using OLS.
Let $v_0(\bm{s}^*_j)$ and $v_1(\bm{s}^*_j)$ be the estimated standard errors of $\tilde{f}_0(\bm{s}^*_j)$ and $\tilde{f}_1(\bm{s}^*_j)$, respectively.
We then treat $f_0(\cdot)$ as a spatial process and consider the ordinary-kriging predictor $\hat{f}_0(\bm{s})$ of $f_0(\bm{s})$, for $\bm{s}\in D$.
Specifically, the ordinary-kriging predictor is obtained using the isotropic exponential covariance model (estimated by maximum likelihood)
based on the following measurement equation:
\[
\tilde{f}_0(\bm{s}^*_j)=f_0(\bm{s}^*_j)+u_0(\bm{s}^*_j);\quad j=1,\dots,m,
\]
where $u_0(\bm{s}^*_j)\sim N(0,v^2_0(\bm{s}^*_j))$; $j=1,\dots,m$, are independent noise variables.
Similar treatment is applied to $f_1(\bm{s})$,
and obtain the ordinary-kriging predictor $\hat{f}_1(\bm{s})$ of $f_1(\bm{s})$, for $\bm{s}\in D$.

\subsection{Spatial prediction based on calibrated AirBox data}

Utilizing the model given by \eqref{eq:data1}, \eqref{eq:calibration} and \eqref{eq:model},
the best linear predictor of $y^*_t(\cdot)$
given $f_0(\cdot)$, $f_1(\cdot)$, $\bm{\theta}_t$ and $\bm{a}$ is
    \begin{align}
      \tilde{y}^*_t(\bm{s}; f_0,f_1, & \bm{\theta}_t,\bm{a})
    \equiv \mathrm{E}(y^*_t(\bm{s})|\bm{z}_t)\notag\\
    =&~ f_0(\bm{s})+f_1(\bm{s})\big(\bm{\varphi}(\bm{s})'\bm{\alpha}_t+\bm{x}_t(\bm{s})'\bm{\beta}_t\big)\notag\\
    &~ +f_1(\bm{s})\bm{c}_t(\bm{s})\big(\bm{\Sigma}_{\eta t}+\bm{\Sigma}_{\varepsilon t}\big)^{-1}(\bm{z}_t-\bm{\Phi}_t\bm{\alpha}_t-\bm{X}_t\bm{\beta}_t);\quad
      \bm{s}\in D,\,t=1,\dots,T,
      \label{eq:ok2}
    \end{align}
where $\bm{\Sigma}_{\eta t}$ is an $n\times n$ matrix with the $(i,j)$-th entry $v^2_t\exp\big(-\|\bm{s}_i-\bm{s}_i\|/\lambda_t\big)$, and
$\bm{\Sigma}_{\varepsilon t}\equiv\mathrm{diag}\big(\sigma_{\varepsilon t}^2(\bm{s}_1),\dots,\sigma_{\varepsilon t}^2(\bm{s}_n)\big)$.
The corresponding mean-squared prediction error (i.e., kriging variance) for $\bm{s}\in D$ and $t=1,\dots,T$ is
    \begin{equation}
    \mathrm{E}\big(\tilde{y}^*_t(\bm{s};f_0,f_1,\bm{\theta}_t,\bm{a})-y_t(\bm{s})\big)^2=f_1(\bm{s})^2\big\{v^2_t-\bm{c}_t(\bm{s})'
    \big(\bm{\Sigma}_{\eta t}+\bm{\Sigma}_{\varepsilon t}\big)^{-1}\bm{c}_t(\bm{s})\big\}.
    \label{eq:okvar2}
    \end{equation}

\noindent After plugging-in the estimated $\hat{f}_0(\cdot)$, $\hat{f}_1(\cdot)$, $\hat{\bm{\theta}}_t$, and $\hat{\bm{a}}$ in \eqref{eq:ok2},
the proposed predictor of $y^*_t(\bm{s})$ for $\bm{s}\in D$ based only on AirBox data is given by
\begin{equation}
\tilde{y}^*_t(\bm{s};\hat{f}_0,\hat{f}_1,\hat{\bm{\theta}}_t,\hat{\bm{a}});\quad \bm{s}\in D,\,t=1,\dots,T,
\label{eq:ok3}
\end{equation}
where $\hat{\bm{\theta}}_t\equiv(\hat{\bm{\alpha}}'_t,\hat{\bm{\beta}}'_t,\hat{v}^2_t,\hat{\lambda}_t)'$; $t=1,\dots,T$.

\subsection{Selection of $K$}
\label{sec:selection}

As demonstrated in Huang \textit{et al}.~(2018), the spatial prediction is not much affected by $K$,
since both the basis functions $\bm{\varphi}(\cdot)$ and the spatial process $\eta_t(\cdot)$ compete to capture $y_t(\cdot)$.
Similar to Huang \textit{et al}.~(2018), we select $K=25$ so that the function in the projected space accounts for about 50\% of the variation in the AirBox data.
Alternatively, $K$ can be selected by using the conditional Akaike's information criterion of Vaida and Blanchard (2005)
or cross validation.

\subsection{Spatial prediction combining EPA and AirBox data}
\label{sec:combine}

For the model given by \eqref{eq:data1}-\eqref{eq:model},
the best linear predictor of $y^*_t(\bm{s})$ incorporating both $\bm{z}_t$ and $\bm{z}^*_t$
with given $f_0(\cdot)$, $f_1(\cdot)$, $\bm{\theta}_t$ and $\bm{a}$ is
    \begin{align}
      \hat{y}^*_t(\bm{s};
    \,&  f_0,f_1,\bm{\theta}_t,\bm{a})\equiv\mathrm{E}(y^*_t(\bm{s})|\bm{z}_t,\bm{z}^*_t)\notag\\
    =&~ f_0(\bm{s})+f_1(\bm{s})\big(\bm{\varphi}_t(\bm{s})'\bm{\alpha}_t+\bm{x}_t(\bm{s})'\bm{\beta}_t\big)\notag\\
  &~ +
      f_1(\bm{s})\bm{c}^*_t(\bm{s})'
      \left(
      \left(
     \begin{matrix}
      \bm{F}_1 & \bm{0}\\
      \bm{0} & \bm{I}
      \end{matrix}
      \right)  \bm{\Sigma}^*_{\eta t}      \left(
     \begin{matrix}
      \bm{F}_1 & \bm{0}\\
      \bm{0} & \bm{I}
      \end{matrix}
      \right)
     +\left(
      \begin{matrix}
      \sigma^2_{\xi t}\bm{I} & \bm{0}\\
      \bm{0} & \bm{\Sigma}_{\varepsilon t}
      \end{matrix}
      \right)\right)^{-1}\notag\\
    &~ \times\left(
      \begin{matrix}
      \bm{z}^*_t-\bm{f}_0-\bm{F}_1(\bm{\varphi}(\bm{s}^*_1),\dots,\bm{\varphi}(\bm{s}^*_m))'\bm{\alpha}_t-
      \bm{F}_1(\bm{x}_t(\bm{s}^*_1),\dots,\bm{x}_t(\bm{s}^*_m))'\bm{\beta}_t\\
      \bm{z}_t-(\bm{\varphi}(\bm{s}_{1}),\dots,\bm{\varphi}(\bm{s}_{n}))'\bm{\alpha}_t-
      (\bm{x}_t(\bm{s}_{1}),\dots,\bm{x}_t(\bm{s}_{n}))'\bm{\beta}_t
      \end{matrix}
      \right),
      \label{eq:calibrate}
    \end{align}

\noindent for $\bm{s}\in D$ and $t=1,\dots,T$, where
    \begin{align*}
      \bm{c}^*_t(\bm{s})
    \equiv&~\big(f_1(\bm{s}^*_1)v^2_t\exp\big(-\|\bm{s}-\bm{s}^*_1\|/\lambda_t\big),\dots,f_1(\bm{s}^*_m)v^2_t\exp\big(-\|\bm{s}-\bm{s}^*_m\|/\lambda_t\big),\bm{c}'_t(\bm{s})\big)',\\
      \bm{\Sigma}^*_{\eta t}
    \equiv&~ \mathrm{var}\big(\eta_t(\bm{s}^*_1),\dots,\eta_t(\bm{s}^*_m),\eta_t(\bm{s}_1),\dots,\eta_t(\bm{s}_n)\big),
    \end{align*}

\noindent $\bm{f}_0\equiv(f_0(\bm{s}^*_1),\dots,f_0(\bm{s}^*_m))'$ and $\bm{F}_1\equiv\mathrm{diag}(f_1(\bm{s}^*_1),\dots,f_1(\bm{s}^*_m))$.
The corresponding mean squared prediction error (i.e., kriging variance) is
    \begin{align}
    \mathrm{E}\big(\hat{y}^*_t(\bm{s};f_0,
    & f_1,\bm{\theta}_t,\bm{a})-y^*_t(\bm{s})\big)^2\notag\\
    =&~ f_1(\bm{s})^2\left\{v^2_t-\bm{c}^*_t(\bm{s})'
    \left(\left(\begin{matrix}
    \bm{F}_1 & \bm{0}\\
    \bm{0} & \bm{I}
    \end{matrix}
    \right)\bm{\Sigma}_{\eta t}^*\left(
    \begin{matrix}
    \bm{F}_1 & \bm{0}\\
    \bm{0} & \bm{I}
    \end{matrix}
   \right)+\left(
    \begin{matrix}
    \sigma^2_{\xi t}\bm{I} & \bm{0}\\
    \bm{0} & \bm{\Sigma}_{\varepsilon t}
    \end{matrix}
    \right)\right)^{-1}
    \bm{c}^*_t(\bm{s})\right\},
    \label{eq:calibrate.var}
    \end{align}
for $\bm{s}\in D$ and $t=1,\dots,T$.

\subsection{Diagnostics}

We conduct model diagnostics using the standardized residuals for $t=1,\dots,T$:
\begin{align}
  r_t(\bm{s}_i)
\equiv&~ \frac{z_t(\bm{s}_i)-\hat{y}_t\big(\bm{s}_i;\hat{f}_0,\hat{f}_1,\hat{\bm{\theta}}_t,\hat{\bm{a}}\big)}
  {\sigma_t\big(\bm{s}_i;\hat{f}_0,\hat{f}_1,\hat{\bm{\theta}_t},\hat{\bm{a}}\big)};\quad i=1,\dots,n,
\label{eq:res1}
\end{align}

\noindent where $\hat{y}_t(\bm{s};f_0,f_1,\bm{\theta}_t,\bm{a})\equiv f_1(\bm{s})^{-1}\big\{-f_0(\bm{s})+\hat{y}^*_t(\bm{s};f_0,f_1,\bm{\theta}_t,\bm{a})\big\}$; $\bm{s}\in D$,
\begin{align*}
  \sigma^2_t(\bm{s}_i;f_0,f_1,
& \bm{\theta}_t,\bm{a})
\equiv \mathrm{var}(z_t(\bm{s}_i)-\hat{y}_t(\bm{s}_i;f_0,f_1,\bm{\theta}_t,\bm{a}))\notag\\
=&~ (\bm{0},\bm{e}'_i\bm{\Sigma}_{\varepsilon t})
   \left(\left(\begin{matrix}
    \bm{F}_1 & \bm{0}\\
    \bm{0} & \bm{I}
    \end{matrix}
    \right)\bm{\Sigma}_{\eta t}^*\left(
    \begin{matrix}
    \bm{F}_1 & \bm{0}\\
    \bm{0} & \bm{I}
    \end{matrix}
   \right)+\left(
    \begin{matrix}
    \sigma^2_{\xi t}\bm{I} & \bm{0}\\
    \bm{0} & \bm{\Sigma}_{\varepsilon t}
    \end{matrix}
    \right)\right)^{-1}
      \left(
      \begin{matrix}
      \bm{0}\\ \bm{\Sigma}_{\varepsilon t}\bm{e}_i
      \end{matrix}
      \right),
\end{align*}

\noindent and $\bm{e}_i$ is the $i$-th column of $\bm{I}_n$.
Note that for $t=1,\dots,T$, we have $r_t(\bm{s}_i)\sim N(0,1)$
if $\hat{f}_0(\cdot)$, $\hat{f}_1(\cdot)$, $\hat{\bm{\theta}}_t$ and $\hat{\bm{a}}$ in \eqref{eq:res1} are replaced by their corresponding true parameters.

\section{Data analysis results}

We applied our method developed in Sections \ref{sec:model}-\ref{sec:combine} to EPA and AirBox data for the year 2020.
There are about respectively  22.2\% and 19.4\% missing observations in the EPA and the AirBox data.
We first did some data cleaning by removing a small portion of unusual PM$_{2.5}$ data that are either negative or larger than 1000 (in ppm) in both datasets.
Among $366\times 24=8784$ hours in the year 2020,
we identified $T=6709$ hours with non-missing observations in at least 500 AirBox locations and 50 EPA locations for model fitting and calibration.
We computed $\hat{\bm{\beta}}_t$,  $\hat{v}_t$ and $\hat{\lambda}_t$ at each hour $t=1,\dots,T$ in 2020 using the proposed method in
Sections \ref{sec:estimation1} and \ref{sec:estimation2} with no covariates $\bm{X}_t$.
We estimated $\bm{a}$ using the method introduced in Section \ref{sec:estimation3}.
Then we estimated $f_0(\cdot)$ and $f_1(\cdot)$ for each month separately using the method described in Section \ref{sec:estimation4}.
The month-wise calibrated functions of intercept and slope are shown in Figures \ref{fig:intercept} and \ref{fig:slope}, respectively.
We can see that both functions vary smoothly in space and time due to
changes in chemical compositions of PM$_{2.5}$ and some other factors, such as
seasonal climate patterns.
The estimated slopes are all less than one because we target measurements from EPA stations located around 10 meters in height, which
tend to produce lower PM$_{2.5}$ values than AirBoxes.
The whole calibrate procedure is computationally fast;
it took less than one hour to obtain $\hat{f}_0(\cdot)$ and $\hat{f}_1(\cdot)$ for each month
(on a PC with AMD Ryzen Threadripper 2920X 12-Core Processor and 64 GB RAM).

\begin{figure}[tb]\centering
\begin{tabular}{cccccc}
\!\!\!January & \!\!\!Februry & \!\!\!March & \!\!\!April & \!\!\!May & \!\!\!June\\
\!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-01.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-02.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-03.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-04.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-05.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-06.png}\\
\!\!\!July & \!\!\!August & \!\!\!September & \!\!\!October & \!\!\!November & \!\!\!December\\
\!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-07.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-08.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-09.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-10.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-11.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f0-12.png}
\end{tabular}
\caption{Month-wise calibrated intercepts for 2020.}
\label{fig:intercept}
\end{figure}

\begin{figure}[tbh]\centering
\begin{tabular}{cccccc}
\!\!\!January & \!\!\!Februry & \!\!\!March & \!\!\!April & \!\!\!May & \!\!\!June\\
\!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-01.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-02.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-03.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-04.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-05.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-06.png}\\
\!\!\!July & \!\!\!August & \!\!\!September & \!\!\!October & \!\!\!November & \!\!\!December\\
\!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-07.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-08.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-09.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-10.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-11.png}
& \!\!\!\!\!\includegraphics[scale=0.16,trim={0cm 0cm 0cm 0cm},clip]{f1-12.png}
\end{tabular}
\caption{Month-wise calibrated slopes for 2020.}
\label{fig:slope}
\end{figure}

We did a diagnostic check using the standardized residuals of \eqref{eq:res1}.
Ideally, if the model fits the data perfectly, the standardized residuals are approximately standard-normal distributed.
However, it is almost impossible to model the AirBox data perfectly due to many outliers (e.g., some people put their AirBoxes indoors or close to some emission sources,
which are likely to produce unusual small or large measurements, respectively).
Figures \ref{fig:diagnostic}(a) and (b) show the median and the MAD of the standardized residuals at each AirBox location.
The median values are all around zero, showing that the proposed method exhibits a small bias in prediction.
However, the MADs vary in space and are mostly smaller than one, indicating that our method tends to be more conservative in producing prediction intervals.

\begin{figure}[tbh]\centering
\begin{tabular}{cc}
  \includegraphics[scale=0.32,trim={0cm 0cm 0cm 0cm},clip]{geomu.png}
&  \includegraphics[scale=0.32,trim={0cm 0cm 0cm 0cm},clip]{geomad.png}\\
(a) & (b)
\end{tabular}
\caption{(a) Location-wise medians of the standardized residuals; (b) Location-wise MADs of the standardized residuals.}
\label{fig:diagnostic}
\end{figure}

We also examined the prediction performance among various methods for each month, indexed by $\mathcal{M}_1,\dots,\mathcal{M}_{12}\subset\{1,\dots,T\}$, separately.
Specifically, for each hour $t\in\mathcal{M}_j$, we randomly divided the EPA data (on the main island with 74 stations)
into the training data $\bm{z}^*_t$ (consisting of 2/3 of non-missing observations with various sizes)
and set the remaining data $\bm{z}^{**}_t\equiv\big\{z^{**}_t(\bm{s}^{**}_{t1}),\dots,z^{**}_{t}(\bm{s}^{**}_{t m_t})\big\}$ with $m_t$ locations for testing purpose.
We estimated $\bm{\beta}_t$, $v_t$ and $\lambda_t$ by $\hat{\bm{\beta}}_t$, $\hat{v}_t$ and $\hat{\lambda}_t$ based on $\bm{z}_t$ as before.
But for $j=1,\dots,12$, we computed the estimators of $\bm{a}$, $f_0(\cdot)$ and $f_1(\cdot)$ based only on $\{\bm{z}^{**}_t:t\in\mathcal{M}_j\}$ and $\{\bm{z}_t:t\in\mathcal{M}_j\}$.
We evaluated the prediction performance using the root mean-squared prediction error (RMSPE) criterion based on the test data $\{\bm{z}^{**}_t\}$:
\[
\mathrm{RMSPE}(\mathcal{M}_j)\equiv\bigg\{
\frac{1}{\sum_{t\in\mathcal{M}_j}m_t}\sum_{t\in\mathcal{M}_j}\sum_{k=1}^{m_t}\big|\tilde{\tilde{y}}^*_t(\bm{s}_{tk})-z^{**}_t(\bm{s}_{tk})\big|^2\bigg\}^{1/2};\quad j=1,\dots,12,
\]
where $\tilde{\tilde{y}}^*_t(\bm{s}_{tk})$ is a generic predictor of $y^*_t(\bm{s}_{tk})$; $k=1,\dots,m_t$, $t=1,\dots,T$.

We compared among six methods:
\begin{enumerate}
\item[M1] Apply the predictor \eqref{eq:uk} based on AirBox data alone with no calibration.
\item[M2] Apply the predictor \eqref{eq:ok3} based on AirBox data alone with a monthly global calibration procedure.
  Specifically, $\hat{f}_0(\cdot)$ and $\hat{f}_1(\cdot)$ in \eqref{eq:ok3} are replaced by $\tilde{f}^{(g)}_0(\cdot)$ and $\tilde{f}^{(g)}_1(\cdot)$ in \eqref{eq:OLS}.
\item[M3] Apply the predictor \eqref{eq:calibrate} combining EPA and AirBox data with a monthly global calibration procedure.
  Specifically, $f_0(\cdot)$ and $f_1(\cdot)$ in \eqref{eq:calibrate} are replaced by $\tilde{f}^{(g)}_0(\cdot)$ and $\tilde{f}^{(g)}_1(\cdot)$ in \eqref{eq:OLS}, and
  $\bm{\theta}_t$'s and $\bm{a}$ in \eqref{eq:calibrate} are replaced by $\hat{\bm{\theta}}_t$'s and $\hat{\bm{a}}$.
\item[M4] Apply the predictor \eqref{eq:ok3} based on AirBox data alone with the proposed spatially adaptive calibration procedure for each month.
 \item[M5] Apply the predictor \eqref{eq:calibrate} combining EPA and AirBox data with the proposed spatially adaptive calibration procedure
   for each month,
  where $f_0(\cdot)$, $f_1(\cdot)$, $\bm{\theta}_t$'s and $\bm{a}$ in \eqref{eq:calibrate} are replaced by
  $\hat{f}_0(\cdot)$, $\hat{f}_1(\cdot)$, $\hat{\bm{\theta}}_t$'s and $\hat{\bm{a}}$, respectively.
\item[M6] Apply ordinary kriging by using the isotropic exponential covariance model (including the nugget effect) based on EPA data only for each hour,
  where the model parameters are estimated by maximum likelihood.
\end{enumerate}

We repeated the whole procedure by randomly decomposing EPA data into training data and test data 100 times,
from which we obtained 100 RMSPE values for each method at each month.
The results are summarized as boxplots in Figure~\ref{fig:rmspe}, separately for each month.
Overall, the RMSPE values are larger in the winter (with usually higher PM$_{2.5}$ values) than in the summer
(with usually lower PM$_{2.5}$ values).
Method M1 with no calibration performed considerably worse than all the other methods.
Methods M2 and M3, which apply a global calibration, improved over Method M1 by about 32\% to 68\%.
But they were outperformed by the proposed M4 and M5 by about 3\% to 24\%,
showing the advantage of applying spatially adaptive calibrations.
Although Method M6 (utilizing high-quality EPA data) performed better than Method M1 (using only AirBox data with no calibration),
it was outperformed by M2 and M3 in almost all months except in December.
Interestingly, Method M2 performed almost the same as Method M3, and
Method M4 performed only less than 1\% worse than Method M5,
indicating that once the calibration curves are established,
we no longer require EPA data unless for locations very close to EPA stations.
Consequently, the AirBox network can almost replaces the EPA network after applying the proposed calibration procedure for PM$_{2.5}$ predictions.

\begin{figure}[bt]\centering
\!\!\includegraphics[scale=0.245,trim={0cm 0cm 0cm 0cm},clip]{rmspe.png}
\caption{Boxplots of root mean-squared prediction errors in various months for six different methods: (M1) AirBox data only with no calibration; (M2) AirBox data only with a global calibration procedure;
(M3) A combination of AirBox and EPA data with a global calibration procedure; (M4)  AirBox data only with the proposed spatially adaptive calibration method;
(M5) A combination of AirBox and EPA with the proposed spatially adaptive calibration method, (M6) EPA data only.}
\label{fig:rmspe}
\end{figure}

\section{Summary}

The AirBox network, consisting of low-cost microsensors, provides a new way to monitor PM$_{2.5}$ at a high spatial resolution that is not possible by traditional monitoring stations.
However, its usefulness has been suspective
since measurements from AirBoxes are not accurate with many outliers, have high variability,
and are highly affected by local environmental conditions.
This paper develops an effective calibration procedure to relieve the concern.
Unlike commonly used calibration techniques, our method does not require putting AirBoxes side by side at monitoring stations.
It automatically considers local environmental conditions by borrowing information from nearby monitoring stations using a spatial varying-coefficients model.
In addition, the proposed method accounts for various aspects of data all in a regression framework, which is easy to understand and implement.

Although our model uses many parameters to describe high complexity in the dataset due to highly complex topographical conditions,
climate patterns, and pollution source distributions in Taiwan,
the complete calibration procedure is fast.
Once the calibrated model is established, we can calibrate all AirBoxes and obtain a PM$_{2.5}$ predicted map in real-time,
even if some AirBoxes are newly added to the network.
In addition, the calibration procedure is not necessary to implement frequently.
It requires to update at most weekly (or monthly) or if some significant changes in PM$_{2.5}$ chemical compositions occur somewhere.

More and more AirBoxes keep adding to the network, enabling us to obtain the PM$_{2.5}$ map at a higher spatial resolution.
Consequently, the AirBox network has great potential to detect new emission sources and help government agencies to make proper control strategies.
It is an exciting but challenging problem.
For example, it is required to distinguish emission contributions from existing sources and outlying measurements.
We consider it an important topic for future research.

\section*{References}

\begin{description}
\item Huang, G., Chen, L.-J., Hwang, W.-H., Tzeng, S.~and Huang, H.-C.~(2018).
  Real-time PM2.5 mapping and anomaly detection from AirBoxes in Taiwan, \textit{Environmetrics},
  \textbf{29}, \url{https://doi.org/10.1002/env.2537}
\item Huber, P.~J.~and Ronchetti, E.~M.~(2009). \textit{Robust Statistics}, 2nd edition, Wiley, New York.
\item Rousseeuw, P.~J.~and van Driessen, K.~(1999). A fast algorithm for the minimum covariance determinant estimator,
  \textit{Technometrics}, \textbf{41}, 212--223.
\item Tzeng, S.~and Huang, H.-C.~(2018). Resolution adaptive fixed rank kriging, \textit{Technometrics}, \textbf{60}, 198--208.
\item Vaida, F.~and Blanchard, S.~(2005). Conditional Akaike information for mixed-effects models, \textit{Biometrika},
  \textbf{92}, 351--370.
\end{description}

\end{document}

redpajama_set_name: RedPajamaArXiv


text:
People are talking about —
— how a group of Karachi University students from the Department of Visual Studies have come up with a design to build low-cost, sustainable, movable houses and according to them, these innovative, affordable houses could prevent the displacement of people in the event of floods in future. People say the government should test these lightweight, extremely low-budget houses which are made up of bamboo, reed, reusable plastic and used tyres and then build them because one house will only cost between Rs50,000 and Rs100,000.
— the announcement by National Accountability Bureau (NAB) that it will not take up corruption cases that involve an amount of less than Rs500 million. People say this means that any case of graft taken, or received, that is even a rupee less than this amount will not be considered as corruption and the persons involved will be able to go scot free, with the knowledge that any amount more than this sum can be received or given twice!
— the arbitrary decision taken by the Sindh government to deduct a certain percentage from the salary of government servants for flood relief and how it has caught the employees by surprise. People say donations should be on a voluntary basis and this deduction does not make any sense as most of the poor government employees have suffered during the rains and floods and they themselves are waiting for help to rebuild their damaged houses and resettle their families.
— the suggestion about making numerous lakes at the foothills of the Sulaiman range and filling them up with hill torrents to increase the ground water table in millions of acres of dry virgin land. People say it will be like storing water to be used when we need it and it will be a thousand times cheaper than building a dam, while avoiding the kind of devastation that we have seen this year. Dams are fine, but liable to break.
— how the residents of Khairpur Nathanshah were told not to leave as there was little chances of flooding, assured by political leaders that they would be present to protect them, yet an alert was issued late at night, telling them to leave. People say villagers rushed to save their lives; the transport mafia took advantage of the panic and increased fares, while officials who had made tall claims were sound asleep, so who should be held responsible for the whole mess?
— the fact that researchers have already made the connection between climate change and how it destroyed the Indus Valley Civilization 4,000 years ago. People say that today, according to experts, Pakistan is facing an existential crisis emanating from rapid climate change, so it must bring global and South nations together to ask for debt relief, while the international community must jointly assist countries facing climate catastrophes so as to place the world's well-being ahead of fossil fuels and profit.
— the sad fact that torture is yet to be criminalized in Pakistan as there is no mention of it in the PPC or the CrPC and though the Police Order 2002, under which the Punjab Police functions, does stipulate penalties against police officers who inflict 'violence or torture' upon anyone in their custody, there is no definition of torture, which is a critical omission. People say lawmakers must step up to make torture unacceptable, with severe repercussions for those who resort to it. — I.H.
Islamabad : Lower division clerks at different Islamabad model colleges have resented out-of-turn promotions of some...
Islamabad : Deputy Chairman Senate Mirza Muhammad Afridi has said that the real estate sector is playing a key role in...
Australian High Commissioner Neil Hawkins also visited the AEO Education Expo Islamabad and appreciated AEO...
Islamabad : Islamabad Model College for Girls, , F-10/2 hosted Inter Collegiate Drama, Self-Grooming and Computer...
Islamabad : The federal government is striving to introduce reforms to build great empowerment of women with strong...
Islamabad : Federal Minister of Education & Professional Training Rana Tanveer Hussain while addressing the...

redpajama_set_name: RedPajamaCommonCrawl


Durham restaurant Bistro 21 is welcoming back a couple of old friends who have been 'down under' to freshen up their food and hospitality, knowledge and skills.
Durham restaurant Bistro 21 is welcoming back a couple of old friends who have been down under to freshen up their food and hospitality, knowledge and skills.
Robbie Bell, 30 of Gateshead, returns from Australia to become head chef of the restaurant, at Aykley Heads, Durham, after working in two of Sydneys most popular and prestigious restaurants.
He is joined by girlfriend Rebecca Tofield, who has been appointed assistant manager.
Bistro 21, part of the 21 Hospitality Group led by renowned restaurateur Terry Laybourne, was recently named Highest Quality Assured and Local Produce Champion at the TasteDurham awards, hosted by tourism agency Visit County Durham.
Robbie joined the 21 Hospitality Group in 2003, developing his talents first as the junior sous chef at Newcastles Cafe 21. He moved to Jesmond Dene House Hotel as an integral part of the opening team, where he became resident sous chef.
After arriving in Sydney a year ago, Robbie gained six months experience in Quay, voted Australias best restaurant 2009/10. For his final six months, Robbie worked alongside famous Australian chef and restaurateur Neil Perry at his new up-market steak house, Rockpool Bar & Grill, winner of the Sydney Morning Herald Good Food Guide 2010 Best New Restaurant.


Text: - Forgot to re-enable ENVY 0x12140324 soundcard, fixed.
- Using menuclass, now menus have images (THX samo79).
- Added MENU_IMG_SIZE tooltype to resize menu images.
- Added new tooltype to prefs window (Menu Image Size).
- About window now has "typical" window title.
- Added 3 new strings in catalog.
- Raised +2 points fontsizes used.
- Changed Bold font to Mono.
- Added ESC key to close/hide MixWindow.


AUCKLAND, New Zealand (July 8, 2002 – Fiji Times)---Te Vaka is heading back to Fiji -- but a little different this time.
The group's third CD, "Nukukehe" ("New Land"), is out in New Zealand and while the music remains infectious and lively, solid for a Suva nightclub, its political too.
Lead singer Opetaia Foa'i though is almost bemused at the idea; his agenda is different.
"I am a spokesman for the Pacific, not in a political way," he told the Fiji Times at his comfortable home in bush clad Titirangi ("edge of heaven"), out in west Auckland.
"My aim is to go down this road and to be among a group of people finding something close to a musical identity for this area.
"I can sit in Paris and listen to the radio and say "ah that's Pacific music'. That's my task, and I cannot use other people's stories, I have to use my own stories."
This time he sings over global warming, change in the Pacific and complex issues like a deadly school fire in Tuvalu and colonization in Tokelau.
Some of it is fun too, like his tribute to Samoan boxer Tavita Tua: O te Tamatoa, Tamatoa o te Pasifika ("this warrior, our warrior of the Pacific").
There is also a piece, Tesema, which celebrates the way in which Samoans in New Zealand who go home for the summer holidays can get two Christmas Days or two New Year Days -- thanks to the International Dateline.
In late August Te Vaka will go to Samoa to perform in the annual Teuila Festival followed by a yet to be confirmed Fiji tour in September – Fiji has a problem in providing suitably large venues. Next year will see the group back in Europe, followed possibly by the U.S.
Foa'i is of mixed Tokelauan and Tuvaluan birth who grew up in the Samoan village of Alamagoto, on the outskirts of the capital, Apia. It is there that the expatriate Tokelauans live. He left for New Zealand as a nine-year-old and only returned, with his family, last year. And for the first time ever, he traveled on to Tokelau and Tuvalu.
Ua leva ou Mataga ese atu Tele mea sui i lou olaga Le mafautau mea Na amata mai ai Ae valau mai e foi atu.
(Left this land a long time ago Much has happened in my life Never looking back To where I came from Still she calls me To return home).
He says getting to see again the places he sang about, bought it through more clearly.
"I thought it was beautiful, it was really exciting."
"It was time and I knew the third album had to be good. I had done the first two albums on my own fantasy island of Alamagoto. I created my own Tokelau island there. I knew it was time to see the real thing."
From Apia the Foa'i family set sail for the three atolls of Tokelau, a New Zealand territory 360 kilometers (216 miles) north of Samoa. The family connection is with the southern most atoll, Fakaofo. Just south of that atoll is another, the lost island of Olohega.
And this is the story with sees Te Vaka become very political, a song called Haloa Olohega ("Poor Olohega").
A monstrous injustice has occurred at Olohega -- or Swains Island as it now appears on maps -- made worse by the fact that so few people live on it.
Tokelauans lived there for thousands of years; they built star mounds and stone houses, still visible to this day.
An American, Eli Hutchinson Jennings, arrived in 1856 and drove away many of the local people. Those that stayed were sold by Jennings, at $10 a head, to the Peruvian slave ship Rosa Patricia and were lost forever. Those that stayed Jennings kept as cheap labor on his copra plantation.
The outrage continues. The Jennings family still claim to own Olohega and will not let Tokelauans back. They pressured the United States to claim the island as American territory, which they did unilaterally in 1925, although Britain, through New Zealand, claimed Tokelau.
In one of those cynical deals diplomats are good at, in 1979 New Zealand renounced its claim on Olohega while Washington in return renounced their claim on Tokelau. Like all good colonial plots, it was done over the resistance of the very people who were worst affected, the Tokelauans.
The political leaders of Tokelau, the faipule, have not forgotten, as Opetaia found out on his trip.
"I am in close contact with the faipule (of Fakaofo)," he said.
"I knew about it, but as far as I was concerned it was a long time ago. They were telling me they had been trying to start talking about Olohega to get it back."
He discovered that Eli Jenning's Samoan wife, Malia, who had been married earlier, was his great great-great grandmother.
Olohega is firmly in his roots.
"I realize it is a significant thing. It is only a small thing this island, but to Tokelau it is a better place to live, because it is higher."
Last year Te Vaka performed Haloa Olohega at concerts in Hawai'i, and got an angry reaction.
"I had the Jennings family knock on the backdoor of the stage, basically saying 'you better not put the song on the album'."
He says the reaction is because he has written the truth of this tragedy.
"After going and discovering all the history, I felt that at least discussion should begin and what I have done is point out some of the truths that will shock people into movement."
On the CD too is Loimata e Maligi ("Let the Tears Fall Down"), in memory of the 19 young girls who died in a fire at the Motufoua boarding school on Vaitupu, Tuvalu, in March 2000.
Opetaia, who keeps in close contact with the small Tuvaluan community in Auckland, says he recalled how shaken people were by the fire, caused when a candle was knocked over. The girls could not escape the dormitory because they were locked in so that boys could not get at them.
"There were people just scratching themselves because they did not know what to do, the frustration of not knowing what to do," Opetaia says.
"It wasn't as if outsiders came and did it; they did it to themselves. They were locked in and I got that feeling of sadness. I had tears. I sat in the studio and that song came out.... It was all they could do, was to let the tears flow and to let the warmth wash in."


You've worked hard to make your garden the perfect sanctuary, but chances are you don't use it as much as you could. You may only make use of it for some of the year and that's a crying shame! One way to maximise your outdoor space is to purchase a fire pit table to make your garden warm & weather-proof during the cooler winter evenings.
I know what you're thinking; I've thought it too. You buy an expensive set of patio furniture and some years down the line a little piece of plastic has fallen off. It's just an insignificant bit, why would you even bother replacing it?
We all know the feeling when a much-loved piece of furniture breaks. It can literally be devastating. Particularly if that piece of furniture has been the source of many happy memories.
You know how it is, with all that wear and tear in the garden, sometimes patio furniture breaks. You have the choice of paying to get it repaired, throwing it away, or you could fix it yourself! Learn how to wrap a double vinyl strap in this step by step guide and repair your furniture on the cheap.
When you first buy your outdoor patio furniture set it comes ready to look great in your backyard. The finishes are polished, the cushions are fluffed and the feet glides are brand new. However, after a few years of wear and tear the cushions may need new covers and your patio furniture feet protectors may need to be replaced.
In 1972 furniture had that a groovy aesthetic of an Austin Powers film. It was a decade of too much is not enough and give me print patterns! that pushed the boundaries of color combinations beyond what our eyes could handle. It was the year of Nixon, the rise of the mini skirts and the creation of ABBA Mama Mia!


And that's why one's canine teeth are called canine teeth. Yikes.
But, hey, what the heck is that knobby thing on the back of that skull? Is that really the skull of a modern wolf? That looks like an unused prop from an Aliens rip-off.
From a brief google it appears the protuberance is a "feature" in wolf skulls--perhaps it is more pronounced in the ice age specimens.


Who Are You Looking For In Hampton, Minnesota?
Run a search by name for anyone in Hampton, Minnesota & get free white pages information instantly. Hampton, Minnesota white page directory listings include full name, phone number and address.


One scholarship in the amount of 50 000 EUR.
participate as an expert or visitor in the work of committees and council with an advisory vote.
In selecting the qualifying Estonian visiting professor, the scholarship committee shall take into account the alignment of the applicant's academic work with the strategic plans of both the University of Tartu and the individual faculties of the university. The awarding of the scholarship shall be based on the applicant's professional qualifications, achievements and reputation as well as their alignment with the priority research areas submitted by the faculties of the University of Tartu.
approval by the host faculty at the University of Tartu.
The recipients of the Scholarship are publicly announced in the course celebrating the anniversary of the University of Tartu on December 1st.


The Pataudi trophy which comprised of five Test matches England and India has finally come to an end with hosts lifting the trophy after winning the series 4-1. Apart from the second Test at The Lod's, the series has been competitive and the best of the two teams have won the series. Although India fought hard, they lacked a complete team effort in their batting except for in the third Test and in the second innings of the final Test.
For England, it will be a memorable series for two reasons. Firstly, they defeated the ICC No 1 Test side by quite a comprehensive scoreline. Secondly, it is the farewell series for probably their greatest Test batsman, Alastair Cook.
However, batting has been difficult right throughout this series and a lot of credit for that also goes to some fine fast bowling so it was a difficult choice to decide who fits the bill and hence best XI of the series has been made with players who struggled quite a bait but shined in the odd innings during the series. Here is the best XI of these top players.
Before his farewell Test, Alastair Cook wouldn't have made it to best XI, but he Cook redeemed himself in the fifth and the final Test of the series at The Oval when he made scores of 71 and 147 to help his side take some lead in the game contest.
Cook's performance in the final was like a dream farewell for him, but the English team must have hoped hat southpaw could've come back to form a bit earlier in the series. However, one can conclude that his decision to retire post this game removed every bit of clutter from his mind and it meant that for one last time the world could witness the best of him.
Another candidate in this list featuring solely because of his performance in the final Test is KL Rahul. Ahead of the Oval Test, Rahul was desperately searching for runs as despite getting some starts he failed to make a mark. He had begun the tour with a hundred at Old Trafford, but those days started fading away with each passing game.
On Tuesday, KL showed some grit and character as he played a terrific knock of 149 which kept India in the hunt before he was dismissed by an absolute jaffa from Adil Rashid.


text:
Now is the Best Time to Buy Tickets
Make Visiting a Live Event a Reality with SeatRetriever!
Home » Classical » Andrea Bocelli
Andrea Bocelli 2020
Andrea Bocelli Tickets
Before he was a world-renowned singer and songwriter, Andrea Bocelli was a court-appointed lawyer. He spent one year using his law degree, which he earned at the University of Pisa. During his time at law school, he earned money by performing at piano bars in the evenings. His love for performing began decades before, however.
The Italian tenor became interested in music at 6 years old. It was then that he started taking piano lessons, later learning how to play other instruments including the flute, saxophone, trumpet, and guitar. What makes Andrea's already impressive musical resume even more extraordinary is that he has been blind since the age of 12.Read More ...
It was during a football game that Andrea was hit in the eye, suffering a brain hemorrhage that led to his loss of sight. However, his blindness hasn't stopped him from finding joy and success through music. At the ripe age of 14, he won his first song competition at the Margherita d'Oro in Italy with the song "'O sole mio." He has been incredibly successful over the course of his career, recording 15 solo albums, nine complete operas, and three greatest hits albums. To date, he has sold more than 90 million albums worldwide and won several awards, including a Golden Globe Award for Best Original Song for "The Prayer," which he sang with the legendary Celine Dion.
Spectrum Center, Charlotte, US
Metropolitan Opera at Lincoln Center, New York, US
AmericanAirlines Arena, Miami, US
Infinite Energy Arena, Duluth, US
Amalie Arena, Tampa, US
SAP Center, San Jose, US
Hollywood Bowl, Los Angeles, US
Teatro Terme Di Caracalla, Ostia Antica, IT
Teatro Del Silenzio, Lajatico, IT
Piazza Castello Marostica, Marostica, IT
`+event.date+`
`+event.time+`
`+event.eventName+`
`+event.eventPlace+`
`; $('.ticket-list').append(eventElement); displayedElements++; if($("input#total_events").val() == $(".ticket-list > div").length){ $('#displayMoreEvents').css('display','none'); } } if(eventsArray.length < 25){ $('#displayMoreEvents').css('display','none'); }else{ if($("input#total_events").val() == $(".ticket-list > div").length){ $('#displayMoreEvents').css('display','none'); }else{ $('#displayMoreEvents').css('display','inline-block'); displayMoreEvents(); } } });
Notable Performances
Andrea's duet with Celine Dion is certainly one of the highlights of his career. He has also collaborated with Jennifer Lopez, Nelly Furtado, Josh Groban and Placido Domingo on projects.
One of his favorite moments was singing "The Lord's Prayer" for Pope Francis in 2015. It was during the Pope's visit to the United States that Andrea got the chance to perform for him in Philadelphia. Of the experience, Bocelli told TIME magazine,
"Having the chance to sing again in front of the Holy Father, for whom I have deep and sincere devotion, offering my humble contribution as a fervent Catholic, is a great honor for me. St. Augustine notoriously reminds us that singing is an extraordinary form of prayer. And this is my goal, my purpose and my joy: to pray together."
How to Buy Tickets to Andrea Bocelli Shows
Check Seat Retriever often for inexpensive tickets. There's no reason to break the bank in order to see your favorite artists in concert. Find cheap seats at some of the best venues in the country so that you can enjoy hearing Andrea Bocelli in the most authentic way possible.
What's Special?
Not only is Andrea Bocelli an incredible vocalist, but he also impresses as a multi-instrumentalist. And while most of his music falls in the classical and opera genres, he has recorded albums in the pop genre too.
Even those who aren't fans of less contemporary music styles will be overcome with admiration by Andrea Bocelli's talents. Traces of his expansive abilities are found throughout his performances, making them an event to remember.
The Andrea Bocelli Experience
To say that attending an Andrea Bocelli concert is an emotional experience is quite the understatement. His voice has been called one of the best in the world by fellow singers and music industry pros alike. He has a natural gift that has never been hindered by his blindness. If anything, his loss of vision makes his performances all the more touching. His strong faith and positive outlook on life give his songs an extra dose of splendor that inspires audiences everywhere.
If you're looking for an extraordinary musical experience, check Seat Retriever for exclusive deals on tickets to an Andrea Bocelli show. Getting to hear his pure, nearly perfect voice in a live setting is something many people have on their bucket list, and it should be on yours too.
HOTTEST EVENTS
Right Time is Now
Tickets will be the ones you ordered or better.
Make Sure You Have Fun!
Browse Our Huge Selection
MLS Events
Nascar Events
NCAA Football Events
Tennis Events
Check Out Your Favorite Artist
From Broadway to Comedy
See All Theater Tickets
Amazing Festival Tickets
Select Your Favorite Festival
Afropunk Festival
Vans Warped Tour
Basilica Block Party
See All Festival Tickets
All Rights Reserved Seat Retriever - 2020 - US
Cookie Policy Privacy and Terms
SeatRetriever.com wants to supply you with the most affordable tickets online.
The right time to buy seats is now. Call SeatRetriever.com at 866.459.9233
Great Venues
Right Time to Buy
Hamilton Review
Why Us? You may ask why should I buy tickets from a site like SeatRetriever.com. We say, why not? We offer the same tickets as most big-ticket vendors online. You'd be supporting a small business and will get personal support should there be a problem. Our 100% guarantee is worth a lot. Give us a chance and see what we can do for you.


SUBSTITUTE 'John Miers died in London in1780, having maintained a residence there despite , it is believed, having taken a lease on Brtion Ferry House in around 1760 . His elder son Nathanthiel who had been "disowned" by the Quakers for marrying in Church, ran the family's works in south Wales as an ironmaster at Neath until his early death in 1782. The younger son, John, who had been running the London end of the business took over in south Wales. He died in 1787. In his will he left the Miers works jointly to his nephews John Nathaniel Miers and Samuel Fothergill Lettsom but both were under age and therefore did not fully inherit the works until 1799.
John Nathaniel Miers, grandson of the orginal John Miers married into the great Hill family of the Plymouth Iron works at Merthyr Tydfil. When capital was needed in order to expand the business, John Nathaniel Miers advanced £5000 (A quarter of the new total) and became a partner. Soon aferwards, in 1803, the Plymouth company agreed with the Dowlais and Penydarren Iron companies to build a tramroad for their joint use. In 1804 one of Richard Trevethick's high pressure locomotives was constructed at Penydarren and made several trips along the the tramroad before being converted to stainonary use. It is acknowledged to have been the world's first steam locomotive.
John Nathaniel Miers continued to run the Miers family works in partnership with his cousin Samuel Fothergill Lettsom. He served as High Sheriff of Glamorgan in 1808'.
p28 DELETE from 'thus further' to 'dynasties'.


text:
Market specific applications
Industrial Refrigeration & Heating
Best hatching conditions with natural refrigerants
27 Jun 2019 By: Bianca Mueller
Chick hatchery replaces natural gas boiler with efficient high-temperature heat pump
For just over a year, the Van Hulst chick hatchery in Veldhoven (Netherlands) went completely without natural gas. Two-stage heat pumps now supply the heat and cooling needed to maintain the temperature of the chicken eggs. The new solution is climate-friendly, thanks to the use of natural refrigerants and operation with solar electricity – and lowers energy costs by approx. 30,000 euros per year.
Cees Horrevorts, General Manager of the Van Hulst chick hatchery, doesn't take half-measures. When investments are needed, they should be sustainable, long-lasting and environmentally friendly. This principle was applied when the old heating system had to be replaced. The worn-out natural gas boilers (2 x 220 kW) had to be replaced with new, climate-friendly technology. At the same time, an increase in capacity was required to prepare for a facility expansion: Today around 1.1 million eggs are hatched each week and the output was planned to increase in the medium term to over 1.4 million eggs per week.
We wanted a modern solution that would meet future requirements, that we can use for a long time, and that is as climate-friendly as possible,"says Horrevorts.
A heat pump was the solution; one with natural refrigerants with low global warming potential (GWP).
Horrevorts found the ideal partner for his plans: Servex Koel- en Vriestechniek B.V. from the Dutch city of Heibloem. Servex has over 40 years of experience in building refrigeration systems and began to specialise in systems with natural refrigerants about five years ago. The company was already familiar with hatcheries from earlier projects.
Innovative and unique
Despite the many reference systems with natural refrigerants that Servex can provide, every project is different. Different boundary conditions, even new components, and varied capacity requirements make each system unique. Even the heat pump system for Van Hulst is unique. "It is the largest heat pump with natural refrigerants that we have ever built," reports Wil Kerkhof, who, together with his brother Marcel Kerkhof, is running the family-owned company Servex in the second generation. "Maybe it's even the largest heat pump of its kind in the Netherlands," he adds. Another special feature: It supplies heat at the unusually high level of approx. 80°C.
Van Hulst head Horrevorts explains why so much heat is needed at such a high temperature: "To hatch fresh eggs, we have to heat them up to 38 degrees Celsius in the first seven days. This is done using large central air handling systems. In addition, we need a great deal of hot water to ensure hygienic conditions in the facility."
Need for heat and refrigeration during hatching
The three two-stage heat pumps are accommodated in this system container. They can supply up to 550 kW of heat at 80°C – even at an ambient temperature of -20°C.
Whereas chicken eggs need heat in the first week, they need cooling in the second and third week. During this time, the embryos in the tightly packed eggs develop so much heat that the air conditioners need to cool them down to maintain the ideal hatching temperature of 38°C. To do this, the new heat pump or the existing cold water generator supplies cool water at 14°C to the central air-conditioning plants.
Due to the simultaneous need for heat and air conditioned cold, the heat pump has a favourable energy balance, as the energy used also operates both media circuits. This alone makes it more efficient than the combination of gas boiler and cold water generator. In addition, gas boilers could only provide one kilowatt hour of thermal energy per kilowatt hour of fuel. The heat pump system, on the other hand, supplies significantly more thermal energy for every kilowatt hour of electricity used.
Increased capacity, higher efficiency
In addition to an increase in energy efficiency, Van Hulst also aimed to increase its thermal output from 440 kW to 550 kW (at 80°C flow temperature) in view of the upcoming capacity expansion. Furthermore, the customer required trouble-free operation in an extremely wide range from minus 20°C to plus 38°C ambient temperature.
We depend on reliable operation throughout the year to create the best conditions for hatching the eggs,"says Horrevorts.
"We wanted to do away with the old natural gas system, so maintaining these limits of application was very important for us."
In order to ensure the desired high availability at extreme ambient temperatures, Servex initially built a test system with low capacity using compressors from the specialist GEA Bock GmbH (Frickenhausen). "We have been working well with GEA Bock for a long time now", says Wil Kerkhof, explaining the choice of the compressor supplier.
The company has extensive experience with natural refrigerants such as carbon dioxide and propane and builds compressors with integrated oil pumps, making them ideal for the Van Hulst project."
Feasibility evaluated with the aid of the test system
The test system was intended to prove the feasibility of a two-stage heat pump for the required operating temperatures and also provide experience with the refrigerant isobutane (R600a). Whereas propane (R290) can be used in the first stage of the heat pump, the second stage had to be geared towards considerably higher condensation and evaporation temperatures – temperatures that could not be achieved with the refrigerants approved by GEA Bock at the time.
Philipp Schmid, who is responsible for application technology at GEA Bock, recalls: "Servex had set up a test system consisting of compressors that were similar to those used today in terms of gas flow and design, but which had less capacity. The HG88e compressors for hydrocarbons, which were planned for final use, were on the verge of series production. Van Hulst wanted these compressors because they offered slightly more capacity and efficiency than their HG8 series predecessors."
Lubrication tested on the test compressor
Using the two-stage test heat pump, Servex, together with its partner GEA Bock, tested whether the capacity could be maintained even at extreme temperatures, how de-icing would behave in the winter and how the compressors would perform. Propane, for which the compressors had already been approved, was used in the first stage. For the second heat pump stage, the partners selected isobutane as the refrigerant because its properties are very well suited to the high temperatures. Both refrigerants have a very low GWP value of three.
However, GEA Bock did not yet have extensive experience with isobutane. This was to be provided by the test system: "We paid particular attention to lubrication," Schmid reports. During trial operation, one oil type proved to be particularly suitable and was therefore selected for the second stage of the system installed at Van Hulst. In addition, GEA Bock modified the oil system to achieve better lubrication.
The heat pump currently in operation at Van Hulst consists of three two-stage systems, i.e. a total of six GEA Bock HG88e/3235-4 S HC compressors. The entire system is set up in containers next to the factory hall. This facilitated installation and the necessary fire protection measures, as both propane and isobutane are highly flammable. However, as the system operates unmanned and is housed in a closed container, the fire protection requirements could easily be met.
High operational reliability
The new heat pump system is located in a container right next to the factory hall.
In addition to the six compressors installed, Van Hulst can also request another compressor to be installed in the container so that a replacement can be carried out quickly in the event of a malfunction. An replacement has already taken place – not because of a defect, however, but to dismantle one of the second-stage compressors after a few months of operation at the GEA Bock facility. The compressor provided a positive result for the very demanding conditions.
For security reasons, the Servex team monitors the operation of the system via remote access to the control equipment. So far, the heat pump has been working flawlessly, even at record temperatures in the summer of 2018. "The only event in recent months has been a warning about oil pressure differential," says Kerkhof. This only required checking the oil level and sensor, and the system continued operating as usual.
Operation mainly under partial load
Usually only one of the three heat pump systems is in operation. Kerkhof: "Given the current heat demand, the capacity of one of the three heat pumps is sufficient to supply 80 degree-water, even at an ambient temperature of only minus ten degrees". This is similar in cooling mode: Already one heat pump is enough to supply the ventilation centres with 14°C cool water with a capacity of up to 200 kW. The three heat pumps therefore operate in alternation. The 10-year operating life contractually guaranteed by Servex should therefore be exceeded by the heat pumps.
As far as energy efficiency is concerned, it is still too early to make concrete statements. According to planning data, annual energy costs should be approx. 30,000 euros lower than in the past, as natural gas is no longer needed and the cold water generators are used less intensively. The additional costs of the heat pump system compared to new natural gas boilers will therefore be amortised within a reasonable time – especially as Van Hulst has received subsidies from the DEI programme (Duurzame Energie Initiatieven / sustainable energy initiative – a programme of the Dutch agency for companies RVO) due to the innovatory value of the system. About half of the additional investment was covered by these subsidies.
Climate-neutral operation with PV electricity
Van Hulst Managing Director Cees Horrevorts is very satisfied with the new heat pump system: "We can now completely do away with fossil fuel natural gas. Moreover, our heat pump is one hundred percent CO2-neutral, because we have recently started using solar power that we generate ourselves for its operation."
Author: Ralf Dunker, specialised journalist, Munich
Overview of the HG series from GEA Bock
The compressors of the HG series from GEA Bock are available in seven sizes with 25 stages and stroke volumes from 5.4 to 281.3 m³/h (at 50 Hz). The compressors optimised for hydrocarbons as refrigerants – the HC versions – offer a long service life and, compared to the models for synthetic refrigerants, are characterised by a special oil charge and further adaptations to meet the requirements of hydrocarbons. The manufacturer recommends the use of an oil sump heater (accessory) and a thermal protection thermostat (accessory) and also offers the electronic motor protection INTG69 G as an accessory pack for installation in the switch cabinet.


An engagement ring is a memento that represents a promise to your loved one. The Wedding Ring Shop helps you pick the ring they'll cherish forever. These gorgeous engagement rings have been crafted by the world's most adored jewelers like Tacori. Tacori offers this perfect ring that is made to last. Find comfort in knowing you'll be able to explore all the products you love located right here in Honolulu, Hawaii.
The 2646-3RDR75Y is a milgrain, vintage style ring that is loved by all. This halo ring matches any outfit, especially a wedding dress. The 18k yellow gold design is simple yet bold. Watch her fawn as she looks in delight at the round center stone. Kept in a prong setting, the exquisite stone sits majestically on the band. The 0.53 ct diamonds are taken and delicately carved into round shapes. The center stone is not included (sold separately).
The Wedding Ring Shop in Honolulu caters to any type of ring preference. We ensure that we can help you choose the perfect ring for your loved one. The Wedding Ring Shop is proud to offer a vast collection of styles that you will adore.


text:
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    android:paddingBottom="@dimen/activity_vertical_margin"
    android:paddingLeft="@dimen/activity_horizontal_margin"
    android:paddingRight="@dimen/activity_horizontal_margin"
    android:paddingTop="@dimen/activity_vertical_margin" >

    <TextView
        android:id="@+id/title_text"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_alignParentTop="true"
        android:layout_centerHorizontal="true"
        android:layout_marginTop="44.0dip"
        android:text="@string/title"
        android:textAppearance="?android:textAppearanceLarge" />

    <Button
        android:id="@+id/toggle_garage_button"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_below="@id/title_text"
        android:layout_centerHorizontal="true"
        android:layout_marginTop="98.0dip"
        android:text="@string/toggle_garage" />

    <TextView
        android:id="@+id/door_is"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_alignLeft="@id/toggle_garage_button"
        android:layout_below="@id/title_text"
        android:layout_marginTop="31.0dip"
        android:text="@string/door_is"
        android:textAppearance="?android:textAppearanceMedium" />

    <TextView
        android:id="@+id/status"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_alignBaseline="@id/door_is"
        android:layout_alignBottom="@id/door_is"
        android:layout_toRightOf="@id/door_is"
        android:paddingLeft="10.0dip"
        android:text="@string/ellipses"
        android:textAppearance="?android:textAppearanceMedium" />

    <Button
        android:id="@+id/close_garage_button"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_alignLeft="@id/toggle_garage_button"
        android:layout_alignRight="@id/toggle_garage_button"
        android:layout_below="@id/toggle_garage_button"
        android:layout_marginTop="44.0dip"
        android:text="@string/close_garage" />

</RelativeLayout>

redpajama_set_name: RedPajamaGithub


text:
Still More Genealogy
Vita brevis; genealogia longa
DIAZ-TIERNEY Genealogy
My Brickwall Ancestor: John KELLY, (1840-1905) – Madness Monday
Per Miriam's splendid suggestion, I'm going to attempt a writeup of one of my current challenges in family history. (I'm not overly fond of the phrase "brick wall".) As a novice genealogist, however, I am modifying Miriam's instructions, in that I am perfectly glad to be told "you should check database thus-and-so." I don't expect anyone to do my work for me. 🙂
What I Want to Know:
John KELLY's parents, and the date and location of his marriage to Johannah LEAHEY.
Known Timeline:
1860 U.S. Census, Miami County, Ohio, population schedule, Brown Twp., p. 41 (handwritten), dwelling 307, family 301, Samuel Sayers household; digital image, Ancestry.com (http://www.ancestry.com : accessed 22 Feb 2009); citing National Archives microfilm publication M653, roll 1010.
John Kelly is listed as a 22yo farm laborer from Ireland with no personal property of value (unlike the other two farm laborers listed with the family).
1870 U.S. Census, Miami County, Ohio, population schedule, Brown Twp., p. 265 (stamped), p. 35 (handwritten), dwelling 296, family 294, John Kelly household; digital image, Ancestry.com (http://www.ancestry.com : accessed 3 May 2008); citing National Archives microfilm publication M593, roll 1244.
John Kelly is listed as a 31yo white male farmer, Irish born, with both parents of foreign birth. He is also listed as a citizen. He is shown with his presumed wife Johannah, age 20, born Ireland, and presumed children Catherine (3, born Canada), Ella (2, born Ohio) and John (3/12, born Ohio).
1880 U.S. Census, Miami County, Ohio, population schedule, Brown Twp., enumeration district (ED) 131, p. 14B, dwelling 131, family 131, John Kelley household; digital image, Ancestry.com (http://www.ancestry.com : accessed 3 May 2008); citing National Archives microfilm publication T9, roll 1049.
John KELLEY, age 40, farmer, is listed with wife Johanna (age 30) and children Catherine (14, born Canada), Ella (12, born Ohio, as are her younger sibs), Johnny (10), Margaret (8), Thomas (6), Mary (4), Edward (3), and farm laborer John PIERCE (50, born in Ireland).
Jan 28 1881, John KELLEY bought a 160 acre farm in Jackson Twp, Darke County. Citation is to the (Darke County) Deed Book 145, p. 502-503.
1888 plat book for Darke County shows the John KELLEY farm.
9 Aug 1894, Mrs. Johannah KELLY dies of heart trouble. Schirack and Schirack Jr., Notes from Union City Times, Death notice of Mrs. Johanna Kelly. Cites 17 Aug 1894 Friday Union City Times. While I'm not detailing the sources here (unless asked — this is becoming quite a pile of words as it is), Johannah has brothers and sisters living in the area, and there are several pointers to Tipperary origins for these LEAHEYs.
1900 U.S. Census, Darke County, Ohio, population schedule, Jackson Twp., enumeration district (ED) 59, sh. 11B (handwritten), dwelling 241, family 242, John Kelly household; digital image, Ancestry.com (http://www.ancestry.com : accessed 3 May 2008); citing National Archives microfilm publication T623, roll 1262.
John Kelly, born Nov 1839, age 60, widowed, born in Ireland of Irish parents. Arrived 1859, in the country for 40 years, naturalized. Occupation farmer; he can read, write, and speak English.
14 Feb 1905, John KELLEY writes his will, signing it with a mark.
16 Feb 1905, John KELLY dies. The Union City Times says "DIED John Kelly, Thursday Feb 16 1905 at residence North Union St, aged 64 years 2 months 23 days; Interment Catholic cemetery."
25 Feb 1905, the will is probated. Citation is to Record of Wills, Darke County Probate Court, volume not noted, p 392-395. Also have copies of applications for letters testamentary and letters of administration, the latter signed by all the heirs (his children).
1920 U.S. Census, Randolph County, Indiana, population schedule, White River Twp., enumeration district (ED) 168, p. 5A, dwelling 127, family 127, Thomas Dillon household; digital image, Ancestry.com (http://www.ancestry.com : accessed 30 Apr 2008); citing National Archives microfilm publication T625, roll 464.
John's oldest daughter Catherine KELLY DILLON is visited by a census taker who helpfully writes "Tipperary" above the "Ireland" listed for the place of birth of both her parents.
Robert E Kelly, passport #304144 issued 7 Jun 1923. Purpose was "pleasure", intended date of travel was early July on the SS Canopic. "U.S. Passport Applications, 1795-1925″. Database and images. Ancestry.com. http://www.ancestry.com : 2007.
John's youngest son Robert Emmett applies for a passport, stating of his father:
… my father John Kelly was born in Ireland and is now deceased; that he emigrated to the United States from the port of Liverpool England on or about 1849; that he resided 57 years, uninterruptedly, in the United States from 1849 to 1906 at Darke County Ohio; that he was naturalized as a citizen of the United States before the Darke County, Ohio ["court" is on the form here, but is lined through] […]
Searches Done:
Phyllis Crick of the Garst Museum in Greenville, OH kindly sent me their surname files on KELLY. She found an 1865 naturalization for a John KELLY, but in Darke County. A check of KELLY naturalizations in Miami County in this time period only turned up a Samuel KELLY. She also sent me the will and letters testamentary for John KELLY, the purchase and sale records for his farm in Darke County, and copies from extraction books of the Union City newspapers.
Ancestry.com search (exact) for KELLY/KELLEY in Brown, Miami, OH in the 1800s in census and voting records shows three groups of KELLYs: a John born in Ireland which I believe is my subject, a group born in Delaware (includes a John and a Samuel), and a group born in New Jersey.
A Footnote.com search for John KELLY between 1845-1880 in Ohio turns up four Civil War pension file index cards. I dismiss two because they are for widows (we know my John outlived his wife). The other two are for invalid pensions. It seems like an unlikely lead (see my Theories, below), but if someone tells me I should check it out, you should also tell me how. 🙂
Searched http://dcoweb.org and http://randolph.dcoweb.org for KELLY and KELLEY. Found an obit for Thomas Francis KELLY, John's son. Found a 1902 directory for Union City, IN which lists on Rural Route 5 "Kelley John — Thos, Ed, Maggie, Mary, Robt., Jose, Celia".
Unchecked Possible Resources:
Request Indiana death certificate (in process).
Query St. Mary's Catholic Church in Union City, IN for records.
Research extant Catholic churches in Brown Twp, Miami OH during the period he was there, and query them for KELLY records.
Suspicions and Theories:
I have two theories for why his eldest daughter was born in Canada, when all her younger siblings were born in Ohio or Indiana. First: he was ducking the Civil War by skipping north over the border. Second, that he went back to Ireland to marry his wife (I don't know where the marriage was, or when, except that Johannah first appears as his wife in the 1870 census, and their oldest child was born in 1865) and returned with her through Canada, taking enough time at it that Catherine was born north of the border. Speculation on these lines very much welcome!
My mother (b. 1946) reports being taken, a couple times, to reunions for ARMSTRONG-KELLY-CULLEN-LEAHEY. Of note is that she remembers the older attendees lamenting that the younger generation didn't have much interest in the reunions, as they didn't know their cousins. This made me very excited when I determined that Johannah LEAHEY KELLY's mother was Catherine ARMSTRONG. It also makes me think of chain migration. I have ample evidence that these LEAHEYs originated in Tipperary, which makes me trust the information from Catherine KELLY DILLON's 1920 census the more.
26 Feb 2009 ambarARMSTRONG, brickwall, County Tipperary, CULLEN, Darke County, DILLON, Indiana, Ireland, KELLY, LEAHEY, Madness Monday, Miami County, Ohio, Randolph County
One thought on "My Brickwall Ancestor: John KELLY, (1840-1905) – Madness Monday"
Apple says:
27 Mar 2009 at 09:39
My James Kelly is one of my brick walls. I believe that he emigrated to Canada and then onto the United States. His first child was also born in Canada and the rest in Jefferson County, NY. It was less expensive for some reason to take the ship to Canada than to come directly to the US. So you may want to look at Canadian ships lists, something I haven't gotten around to yet. I think it more likely that John came over in 1859 than 1849 but you could check the 1851 Canadian census. Another resource you might look for is an old history of the county he settled in, they often listed the rolls of those that served in the Civil War and that might give you a better idea of whether or not to spend the big bucks on a Civil War pension file that may or may not be his.
Previous Previous post: Wordless Wednesday: Nicholas John KOHL and Bertha WEYRICH KOHL, 1945
Next Next post: Tombstone Tuesday: Edward Joseph Kelly, Jr (1915 – 1917)


text:
Doctor's Audell Profile
Margaret Switack Audell , MD
Orange Coast Womens Medical Group
24411 Health Center Dr Ste 200
has been an active medical staff member at Saddleback Memorial Medical Center. Through the years she has served as Chairman of the Womens and Childrens Credentials Committee, Chairman of the Practitioners Well-being Committee, and has been Vice Chief of Staff, and Chief of Staff at Saddleback Memorial Medical Center. It is Dr. Audell's belief that "a patient can be a more active participant in her healthcare when she is informed about her medical status and the different options available to her." She has also served on the California Birth Defects Monitoring Program Advisory Committee, which oversaw the largest birth defects registry in the world. She has been active in the Cooperative of American Physicians-Mutual Protection Trust by serving as a member of the OB/GYN Peer Review Committee, the Obstetrical Claims Review Committee, and she has been a member of their Board of Directors. Dr. Audell received her undergraduate degree from Lewis and Clark College in Portland, Oregon. Then she graduated Georgetown University School of Medicine in Washington, DC, and completed her postgraduate training there as well. Dr. Audell has a special interest in perimenopausal and menopausal women's issues. She enjoys fly fishing with her husband, who is a Geologist.
Languages Spoken: N/A
Georgetown University School Of Medicine Graduated in 1980


Wire Pull, Brushed Brass Finish, Solid Brass.
For a remodel that is bright but not shiny, this is the pull for you.
Comes with 1" 8-32 machine screws. If needed Order 8-32 screw length by Material Thickness + 1/4" for pull.


"SHADES OF DEEP PURPLE" RARE ORIGINAL 1968 UK PROG ROCK LP NICE 1ST PRESSING EX!
Vinyl solid UK quality pressing.
The disc is in a LAMINATED FLIP-BACK cover, complete with Custom Company advertising inner sleeve.
Brilliant Ritchie Blackmore guitar combined with Jon Lord's virtuoso talent on keyboards, this was the original Purple lineup, featuring founder members Rod Evans and Nick Simper.
This was not available for long in this original form before the lable style was changed, this is the FIRST issue format and a first pressing!
The VINYL is WONDERFUL EX shape, FULL SHINE and a couple of fine lines only, only a few very sparse signs of sleeve removal.
Beautiful top quality vinyl with FULL shine!
Classic Yellow & Black 1968 Lables are in clean NEAR MINT- CONDITION. Also, no pen stickers or tears. I can't see any spindle marks at all here.
The LAMINATED 'FLIP-BACK' CARD COVER grades NEAR MINT, a super example ! This has lovely as-pressed shine, very light wear only.
The original Parlophone album advertising inner is included, bright and clean with no wear evident.
The disc will be sent in another plain sleeve to preserve this.
It is a supefb copy of this original issue!
Bid responsibly, knowing all item details.
See my other auctions, there's no extra postage for multiple purchases.


The Northern Cape High Court today ruled in favour of Siamisa Motheo / Maak Die Fondasie Reg / Lungisa Umgangatho – a community based organization of teachers, parents and concerned community members – and 47 parents of learners in Vela Langa Primary School in Upington, by declaring the language policy adopted by the school's governing body (SGB) invalid.
The court also declared that the SGB as the first respondent was in breach of its duty to promote the best interests of the school community and ordered it to consult with parents and affected members of the community within one month before adopting a new language policy.
The applicants had brought an unopposed case before the court about the language policy of the primary school, which they argued ran counter to the provisions of the South African Constitution that specifically guarantee the right to basic education, which includes the right to choose the language of instruction.
This is a significant victory for community members to ensure that school governing bodies, as their elected representatives, make decisions that promote their best interests and protect their constitutional rights.