page_break.md

jupytext	kernelspec
cell_metadata_filter cell_metadata_json encoding formats notebook_metadata_filter text_representation all true # -*- coding: utf-8 -*- ipynb,md:myst all,-language_info,-toc,-latex_envs extension format_name format_version jupytext_version .md myst 0.13 1.11.5	display_name language name Python 3 python python3

Test page break and equation number

using the following headers.json file:

{
    "page_title": "Day 03 quiz",
    "left_header": "Jan. 19, 2021",
    "center_header": "Day 03 quiz",
    "page_margin_top": 1,
    "page_margin_bottom": 1,
    "page_margin_left": 1,
    "page_margin_right": 1 
}

Tests

• page_break

• natural_fill

• equation_number

• equation_ref

• align_equations

(sec:page_break)=

Test page break

+++

Insert the following div to get a forced page break:

<div class="page-break"></div>

+++

(natural_fill)=

Test page fill

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

Pellentesque dapibus suscipit ligula. Donec posuere augue in quam. Etiam vel tortor sodales tellus ultricies commodo. Suspendisse potenti. Aenean in sem ac leo mollis blandit. Donec neque quam, dignissim in, mollis nec, sagittis eu, wisi. Phasellus lacus. Etiam laoreet quam sed arcu. Phasellus at dui in ligula mollis ultricies. Integer placerat tristique nisl. Praesent augue. Fusce commodo. Vestibulum convallis, lorem a tempus semper, dui dui euismod elit, vitae placerat urna tortor vitae lacus. Nullam libero mauris, consequat quis, varius et, dictum id, arcu. Mauris mollis tincidunt felis. Aliquam feugiat tellus ut neque. Nulla facilisis, risus a rhoncus fermentum, tellus tellus lacinia purus, et dictum nunc justo sit amet elit.

(equation_number)=

Test equation number cross reference

$$ \int_\alpha^\beta \cos ( \gamma x ) , dx $$ (eq:labelint)

Breaking page here

+++

(equationref)=

Reference the equation

And here is a reference to equation {eq}eq:labelint

(align_equations)=

Some aligned equations

Q5) From the readings water vapor feedback can be written as:

$$ \begin{align*} f = \left( \frac{\Delta R}{\Delta \mbox{H2O}} \right) \times \left( \frac{\Delta\mbox{H2O}} {\Delta T} \right ) \end{align*} $$(eq:h2o)

Which of the following statements is correct?

$$ \begin{align*} A) \left( \frac{\Delta R}{\Delta \mbox{H2O}} \right ) \mbox{is positive} \left( \frac{\Delta \mbox{H2O}} {\mbox{ΔT}} \right ) \mbox{is positive} \ B) \left( \frac{\Delta R}{\Delta \mbox{H2O}} \right ) \mbox{is positive} \left( \frac{\Delta \mbox{H2O}} {\mbox{ΔT}} \right ) \mbox{is negative} \ C) \left( \frac{\Delta R}{\Delta \mbox{H2O}} \right ) \mbox{is negative} \left( \frac{\Delta \mbox{H2O}} {\mbox{ΔT}} \right ) \mbox{is positive} \ D) \left( \frac{\Delta R}{\Delta \mbox{H2O}} \right ) \mbox{is negative} \left( \frac{\Delta \mbox{H2O}} {\mbox{ΔT}} \right ) \mbox{is negative} \ E) \left( \frac{\Delta R}{\Delta \mbox{H2O}} \right ) \mbox{is negative} \left( \frac{\Delta \mbox{H2O}} {\mbox{ΔT}} \right ) \mbox{is positive} \ \end{align*} $$(eq:feedback)

+++

\begin{align*}
\text{Layer energy equation:} ~~~ & \frac { d E } { d t } = I _ { \downarrow } + I _ { \uparrow }\\
\text{Solar constant:}~~~& S= \frac { S _ { 0 } } { 4 } ( 1 - \alpha )\\
\text{Total grey body flux} ~~~ & I = \varepsilon \sigma T ^ { 4 }\\
&\text{where} ~~~ \sigma = 5.67 \times 10 ^ { - 8 } \mathrm { Wm } ^ { - 2 } \mathrm { K } ^ { - 4 }\nonumber\\
\text{transmissivity tr:}~~~& I _ { \text {transmitted } } = \mathrm { tr } I _ { 0 }\\
\text{reflectity}~ \alpha~~~ & I _ { \text {reflected } } = \alpha I _ { 0 } \\
\text{absorbtivity abs} ~~~ & I _ { \text {absorbed} } = \text{abs} I _ { 0 }\\
\text{Kirchoff's law} ~~ & \varepsilon = \text{abs} \\
\text{$CO_2$ radiative forcing} ~~~& \Delta F = \left(3.8 \mathrm{W} \mathrm{m}^{ - 2 } \right) \frac { \ln ( \text {newp} \operatorname { CO } 2 / \text { origp } \mathrm { CO } 2 ) } { \ln ( 2 ) } \\
\text{Conservation of Energy:}~~~&\alpha \mathrm { I } _ { 0 } + a b s \mathrm { I } _ { 0 } + \mathrm { trI } _ { 0 } = \mathrm { I } _ { 0 }\\
\text{moist static energy:}~~~ & h _ { m } = c _ { p } T + l _ { v } w _ { v } + g z \\
\text{moist adiabatic lapse rate:}~~~&\Gamma = \frac { d T } { d z } = \frac { - g } { c _ { p } + l _ { v } \frac { d w _ { v } } { d T } }\\
\text{hydrostatic balance:}~~~&d p = - \rho g d z \\
\text{mass in a layer in $kg/m^2$:}~~~&M = \int _ { z _ { 1 } } ^ { z _ { 2 } } \rho(z) d z\\
\text{energy in an ocean layer:}~~~&\Delta E=\rho_{w} D c_{w} \Delta T\\
\text{Conservation of energy for layer:}~~~&\frac{d \Delta E}{d t}=\Delta F\\
\text{change of temperature for an ocean layer:}~~~&\frac{d \Delta T}{d t}=\frac{\Delta F}{\rho_{w} c_{w} D}\\
\text{Planck feedback:}~~~&\frac { d I _ { G } } { d T } = \frac { d \left( - \sigma T ^ { 4 } \right) } { d T } = f_{planck} =- 4 \sigma T ^ { 3 } = - 1 / \lambda\\
\text{Conservation of energy with feedback:}~~~&
\frac { \Delta E } { d t } = \Delta F - 4 \sigma T ^ { 3 } \Delta T\\
\text{Climate adjustment to abrupt forcing:}~~~&\Delta T ( t ) = \lambda \Delta F \left( 1 - e ^ { - t / \tau } \right) \\
\text{Climate adjustment timescale:}~~~&\tau = \rho _ { w } c _ { w } D \lambda\\
\text{Climate sensitivity:}~~~&\Delta T = \lambda \Delta F\\
\text{Climage mean temperature budget:}~~~&\rho _ { w } c _ { w } D \frac { d T } { d t } = \Delta F + \sum f _ { n } \Delta T\\
\text{Climate feedback factor:}~~~&f _ { n } = \frac { \Delta R } { \Delta T } = \left( \frac { \Delta R } { \Delta \text { climate } } \right) \left( \frac { \Delta \text { climate } } { \Delta T } \right)\\
\text{Climate sensitivity with feedbacks:}~~~&\lambda = - \frac { 1 } { \sum f _ { n } }
\end{align*}

+++

Quiz 2 constants

\begin{align*}
&\text{1 ppm = 2.1 Gtonnes Carbon = 7.6 Gtonnes $CO_2$}\\
\sigma  &= 5.67 \times 10 ^ { - 8 } \mathrm { Wm } ^ { - 2 } \mathrm { K } ^ { - 4 }\\
c_p  &= 1004\ J\,kg^{-1}\,K^{-1} \\
c_w  &= 4186\ J\,kg^{-1}\,K^{-1} \\
\rho_w &= 1000\ kg\,m^{-3}\\
l_v &= 2.5 \times 10^6\ J\,kg^{-1}
\end{align*}