Chapter 16 Inference for RegressionClimate ChangeThe .docxketurahhazelhurst
Chapter 16: Inference for Regression
Climate Change
The earth has been getting warmer. Most climate scientists agree that one important cause of the warming is
the increase in atmospheric levels of carbon dioxide (CO2), a green house gas. Here is part of a regression
analysis of the mean annual CO2 concentration (CO2) in the atmosphere, measured in parts per thousand
(ppt), at the top of Mauna Loa in Hawaii and the mean annual air temperature (Temp) over both land and
sea across the globe, in degrees Celsius.
Let’s first read the dataset into R
climate <- read.table('Climate_Change.txt', sep = '\t', header = TRUE)
and take a look at the data structure:
str(climate)
## 'data.frame': 29 obs. of 3 variables:
## $ year: int 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 ...
## $ Temp: num 14.2 14.3 14.1 14.3 14.1 ...
## $ CO2 : num 339 340 341 342 344 ...
We see three variables, which are year, Temp (mean annual air temperature) and CO2 (mean annual CO2
concentration), and there are 29 observations in each variable.
We now take Temp as the response variable and CO2 the predictor variable, to study their relationship. To see
if linear regression is appropriate, we make a scatterplot of Temp against CO2
plot(climate$CO2, climate$Temp, xlab = 'CO2 Concentration', ylab = 'Temperature')
340 350 360 370 380
1
4
.1
1
4
.3
1
4
.5
CO2 Concentration
Te
m
p
e
ra
tu
re
It seems reasonable to fit a linear model to the dataset, because both variables are quantitative, the data
points show a linear pattern, and there is no outlier. So, let’s fit the model:
imod <- lm(Temp ~ CO2, data = climate)
1
The summary of the fitted model is given by
summary(imod)
##
## Call:
## lm(formula = Temp ~ CO2, data = climate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.16809 -0.07972 0.00194 0.07013 0.18532
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.707076 0.481006 22.260 < 2e-16 ***
## CO2 0.010062 0.001336 7.534 4.19e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09847 on 27 degrees of freedom
## Multiple R-squared: 0.6776, Adjusted R-squared: 0.6657
## F-statistic: 56.76 on 1 and 27 DF, p-value: 4.192e-08
which contains a lot of information. We see that R2 = 0.6776 and the SD of residuals se = 0.09847 (the
estimator of population standard deviation σ) with 27 degrees of freedom. In Coefficients section we
see the intercept b0 = 10.71 and the slope b1 = 0.01. Their standard errors are SE(b0) = 0.481 and
SE(b1) = 0.00134. Their t-test statistics are t0 = b0/SE(b0) = 22.26 and t1 = b1/SE(b1) = 7.534. Their
corresponding (two-tailed) p-values are very small (<2e-16 and 4.19e-08). As a result, we reject H0 : β1 = 0
and conclude there is a positive correlation between Temp and CO2. The b1 = 0.01 can be interpreted as
follows: The air temperature will increase by 0.01 degrees Celsius on average if the CO2 concentration in the
atmosphere increases by 1 p ...
Jom first guess upgrade in min temp tool (jan 2015)James Brownlee
This is the final paper for the project that I collaborated on with William P. Roeder at the 45th Weather Squadron (45 WS). The goal of this project was to improve the minimum temperature predictions that are made by the 45 WS for space launch operations at the Cape Canaveral Air Force Station (CCAFS) and the Kennedy Space Center (KSC). At the end of this project, the minimum temperature predictions made by the 45 WS were significantly improved, and the 45 WS began using the new minimum temperature algorithm during the 2014/2015 winter season. This project was one major step aimed at improving the minimum temperature tool.
Ultrasonic Range Finder Exporter, Laser Range Finder Manufacturer, Microcontrolled Ultrasonic Range Finder Supplier, Microcontrolled Laser Range Finder India, Obstacle Detection Meter Delhi NCR, Industrial Ultrasonic Range Finder Sonipat. Request For Quote. For More Information Please Logon http://cutt.us/BoOBp
Chapter 16 Inference for RegressionClimate ChangeThe .docxketurahhazelhurst
Chapter 16: Inference for Regression
Climate Change
The earth has been getting warmer. Most climate scientists agree that one important cause of the warming is
the increase in atmospheric levels of carbon dioxide (CO2), a green house gas. Here is part of a regression
analysis of the mean annual CO2 concentration (CO2) in the atmosphere, measured in parts per thousand
(ppt), at the top of Mauna Loa in Hawaii and the mean annual air temperature (Temp) over both land and
sea across the globe, in degrees Celsius.
Let’s first read the dataset into R
climate <- read.table('Climate_Change.txt', sep = '\t', header = TRUE)
and take a look at the data structure:
str(climate)
## 'data.frame': 29 obs. of 3 variables:
## $ year: int 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 ...
## $ Temp: num 14.2 14.3 14.1 14.3 14.1 ...
## $ CO2 : num 339 340 341 342 344 ...
We see three variables, which are year, Temp (mean annual air temperature) and CO2 (mean annual CO2
concentration), and there are 29 observations in each variable.
We now take Temp as the response variable and CO2 the predictor variable, to study their relationship. To see
if linear regression is appropriate, we make a scatterplot of Temp against CO2
plot(climate$CO2, climate$Temp, xlab = 'CO2 Concentration', ylab = 'Temperature')
340 350 360 370 380
1
4
.1
1
4
.3
1
4
.5
CO2 Concentration
Te
m
p
e
ra
tu
re
It seems reasonable to fit a linear model to the dataset, because both variables are quantitative, the data
points show a linear pattern, and there is no outlier. So, let’s fit the model:
imod <- lm(Temp ~ CO2, data = climate)
1
The summary of the fitted model is given by
summary(imod)
##
## Call:
## lm(formula = Temp ~ CO2, data = climate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.16809 -0.07972 0.00194 0.07013 0.18532
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.707076 0.481006 22.260 < 2e-16 ***
## CO2 0.010062 0.001336 7.534 4.19e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09847 on 27 degrees of freedom
## Multiple R-squared: 0.6776, Adjusted R-squared: 0.6657
## F-statistic: 56.76 on 1 and 27 DF, p-value: 4.192e-08
which contains a lot of information. We see that R2 = 0.6776 and the SD of residuals se = 0.09847 (the
estimator of population standard deviation σ) with 27 degrees of freedom. In Coefficients section we
see the intercept b0 = 10.71 and the slope b1 = 0.01. Their standard errors are SE(b0) = 0.481 and
SE(b1) = 0.00134. Their t-test statistics are t0 = b0/SE(b0) = 22.26 and t1 = b1/SE(b1) = 7.534. Their
corresponding (two-tailed) p-values are very small (<2e-16 and 4.19e-08). As a result, we reject H0 : β1 = 0
and conclude there is a positive correlation between Temp and CO2. The b1 = 0.01 can be interpreted as
follows: The air temperature will increase by 0.01 degrees Celsius on average if the CO2 concentration in the
atmosphere increases by 1 p ...
Jom first guess upgrade in min temp tool (jan 2015)James Brownlee
This is the final paper for the project that I collaborated on with William P. Roeder at the 45th Weather Squadron (45 WS). The goal of this project was to improve the minimum temperature predictions that are made by the 45 WS for space launch operations at the Cape Canaveral Air Force Station (CCAFS) and the Kennedy Space Center (KSC). At the end of this project, the minimum temperature predictions made by the 45 WS were significantly improved, and the 45 WS began using the new minimum temperature algorithm during the 2014/2015 winter season. This project was one major step aimed at improving the minimum temperature tool.
Ultrasonic Range Finder Exporter, Laser Range Finder Manufacturer, Microcontrolled Ultrasonic Range Finder Supplier, Microcontrolled Laser Range Finder India, Obstacle Detection Meter Delhi NCR, Industrial Ultrasonic Range Finder Sonipat. Request For Quote. For More Information Please Logon http://cutt.us/BoOBp
Electrical thermal imaging report sample from TICOR. TICOR™ is an android based reporting software system that can generate thermal imaging electrical reports onsite in less than 20 seconds. TICOR™ has been designed so that reporting is undertaken during the inspection through a series of drop down option boxes which gives the thermographer the ability to create instant onsite reports in less than 20 seconds after completion of the inspection.
Fire Monitoring System for Fire Detection Using ZigBee and GPRS SystemIOSRJECE
Wireless Sensor Networks (WSN) is best suited for applications where continuous and long term data acquisition is required. Forest fire monitoring is one of such application where continuous monitoring of temperature and humidity is essential to detect the wildfire. Monitoring forest for wildfire detection is very much necessary to protect environment and to conserve forest wealth and habitats of biodiversity and livelihood of human. This paper presents an algorithm to detect the wildfire based on the changes occurring in humidity and temperature during fire and presents methodology based on ZigBee and GPRS wireless sensor network which provides low cost solution with long life time, low maintenance and good quality service as compared to the traditional method of wildfire detection. The hardware circuitry of proposed solution is based on Arduino board with ATmega328 microcontroller, temperature sensor and humidity sensor along with ZigBee and GPRS modules.
Investigating the Weather impact on Power Outages - Big Data Expo 2019webwinkelvakdag
To accelerate the development towards a Smart Grid, one of the challenges that the Dutch grid operator Liander has is to improve continuous power delivery. Liander has researched the correlation between weather conditions and power outages, which can be further used to predict the outages and take proactive actions to prevent them from happening. Given the large scale of the datasets involved, and potential future use cases, Liander developed several building blocks to analyze the data. To retrieve and redistribute climate and weather data, a generic API was built in Python. It allows its users to quickly attain the desired data in an unambiguous and uniform representation, in the format of their choosing. This API is also used in other analytics, e.g. load forecast. In this presentation we show you what we did, whether it was successful, and what we have learned during the process, as well as our next steps.
Research proposal: Thermoelectric cooling in electric vehicles KristopherKerames
This research proposal describes the theory behind thermoelectric cooling (TEC) in the context of electric vehicle thermal management systems, and describes the experimental setup and error analysis required to study TEC in that context.
Electrical thermal imaging report sample from TICOR. TICOR™ is an android based reporting software system that can generate thermal imaging electrical reports onsite in less than 20 seconds. TICOR™ has been designed so that reporting is undertaken during the inspection through a series of drop down option boxes which gives the thermographer the ability to create instant onsite reports in less than 20 seconds after completion of the inspection.
Fire Monitoring System for Fire Detection Using ZigBee and GPRS SystemIOSRJECE
Wireless Sensor Networks (WSN) is best suited for applications where continuous and long term data acquisition is required. Forest fire monitoring is one of such application where continuous monitoring of temperature and humidity is essential to detect the wildfire. Monitoring forest for wildfire detection is very much necessary to protect environment and to conserve forest wealth and habitats of biodiversity and livelihood of human. This paper presents an algorithm to detect the wildfire based on the changes occurring in humidity and temperature during fire and presents methodology based on ZigBee and GPRS wireless sensor network which provides low cost solution with long life time, low maintenance and good quality service as compared to the traditional method of wildfire detection. The hardware circuitry of proposed solution is based on Arduino board with ATmega328 microcontroller, temperature sensor and humidity sensor along with ZigBee and GPRS modules.
Investigating the Weather impact on Power Outages - Big Data Expo 2019webwinkelvakdag
To accelerate the development towards a Smart Grid, one of the challenges that the Dutch grid operator Liander has is to improve continuous power delivery. Liander has researched the correlation between weather conditions and power outages, which can be further used to predict the outages and take proactive actions to prevent them from happening. Given the large scale of the datasets involved, and potential future use cases, Liander developed several building blocks to analyze the data. To retrieve and redistribute climate and weather data, a generic API was built in Python. It allows its users to quickly attain the desired data in an unambiguous and uniform representation, in the format of their choosing. This API is also used in other analytics, e.g. load forecast. In this presentation we show you what we did, whether it was successful, and what we have learned during the process, as well as our next steps.
Research proposal: Thermoelectric cooling in electric vehicles KristopherKerames
This research proposal describes the theory behind thermoelectric cooling (TEC) in the context of electric vehicle thermal management systems, and describes the experimental setup and error analysis required to study TEC in that context.
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HEAT WAVES AND EFFETCS IN THE INDIAN SUB CONTINENT
1.
2. Data from 1293 weather stations in the country have been
received from the new_csv7d_latlong.csv file.
Of these, 350 are observed stations, while the remaining
stations are forecast stations and city weather stations.
Observed stations provide data for today as well as seven
days of forecast data, while forecast stations only provide
seven days of forecast data.
Station Data
3. To accurately interpolate maximum temperature we use the
observed 12:00 UTC maximum temperature from yesterday for the
morning and the 12:00 UTC maximum temperature from today for
the evening, along with the next five days of forecast data.
We calculate the maximum temperature departure using pentad
normal data from 1991-2020 from CRS Pune and the observed 12:00
UTC maximum temperature for observed stations and also forecast
stations.
The resulting spatial map is also used on the heat wave web-GIS
page. Additionally, the observed maximum temperature and its
departure for the past five days are also available on the web-GIS
page.
Maximum Temperature & Departure
4. Pentad Normal (1991-2020)
In ISSD script, taking Normals of 28 february for 29 february.
CRS Pune has provided pentad normal data with 73 columns for each 5 days.
It will consist of 365 days so when leap year occurs then we have 366 days so for this leap year
we take 28 feb data normal for calculating departure for 29 feb.
12th column of pentad will use for 25th feb to 1st mar (5days). During leap year, it is 25th feb to
1st mar (6days).
5. Similarly, to determine the minimum temperature, we use the
observed 03:00 UTC station data for today's data and combine it with
observed and forecast stations for the next five days of forecast data.
We also calculate the minimum temperature departure using pentad
normal data from 1991-2020 from CRS Pune and the observed 03:00
UTC minimum temperature for observed stations and forecast
stations.
The resulting spatial map is used on the heat wave web-GIS page.
Additionally, the observed minimum temperature and its departure
for the past five days are also available on the web-GIS page.
Minimum Temperature and its Departure
6. To interpolate relative humidity, we use the observed relative
humidity at 12:00 UTC from yesterday and the observed relative
humidity at 03:00 UTC from today for the morning, and the relative
humidity at 12:00 UTC from today for the evening.
The resulting spatial map is then utilized on the heatwave web-GIS
page. Additionally, the observed relative humidity for the past five
days is also available on the web-GIS page.
Relative Humidity (RH)
7. The data collected from 0900UTC synoptic data includes the dry bulb temperature,
wind speed, wind direction, and relative humidity.
Similarly, the forecast data are used for the next five days.
These products are one of the inputs for the generation of heat wave bulletin
including heat index.
09:00UTC Temperature, wind speed, wind
direction and Relative Humidity
8. The observed max temperature and its departure are used to calculate the heat wave /
Severe Heat Wave for today and the forecast max temperature and its departure are
used for the next five days' heat wave / Severe Heat Wave. (Reference: Forecasting
Circular No. 5/2015 (3.7).
Heat wave is considered if maximum temperature of a station reaches at least 40°C or
more for Plains and at least 30°C or more for Hilly regions.
a) Based on Departure from Normal
Heat Wave: Departure from normal is 4.5°C to 6.4°C
Severe Heat Wave: Departure from normal is >6.4°C
b) Based on Actual Maximum Temperature
Heat Wave: When actual maximum temperature ≥ 45°C
Severe Heat Wave: When actual maximum temperature ≥47°C
Criteria for describing Heat Wave for coastal stations
When maximum temperature departure is 4.5°C or more from normal, Heat Wave may be
described provided actual maximum temperature is 37°C or more.
Heat Wave
9. The observed max temperature and minimum departure are used to calculate the
warm night/severe warm night for today and the forecast max temperature and
minimum departure are used to calculate the warm night/severe warm night for the
next five days.
It should be considered only when maximum temperature remains 40°C or more. It may
be defined based on departures or actual minimum temperatures as follows:
Warm night: minimum temperature departure is 4.5°C to 6.4°C
Very warm night: minimum temperature departure is >6.4°C
Warm Night
10. The heat index for today is calculated using the dry bulb temperature and relative
humidity from 0900UTC synoptic data. For the next five days, the heat index is
calculated using the forecast temperature and relative humidity.
Heat index formula: https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
The computation of the heat index is a refinement of a result obtained by multiple
regression analysis carried out by Lans P. Rothfusz and described in a 1990 National
Weather Service (NWS) Technical Attachment (SR 90-23). The regression equation of
Rothfusz is
HI = -42.379 + 2.04901523*T + 10.14333127*RH - .22475541*T*RH - .00683783*T*T -
.05481717*RH*RH + .00122874*T*T*RH + .00085282*T*RH*RH - .00000199*T*T*RH*RH
Where, T is temperature in degrees F and RH is relative humidity in percent. HI is the heat
index expressed as an apparent temperature in degrees F.
Heat Index
11. If the RH is less than 13% and the temperature is between 80 and 112 degrees F, then
the following adjustment is subtracted from HI:
ADJUSTMENT = [(13-RH)/4]*SQRT{[17-ABS(T-95.)]/17}
Where, ABS and SQRT are the absolute value and square root functions, respectively.
On the other hand, if the RH is greater than 85% and the temperature is between 80
and 87 degrees F, then the following adjustment is added to HI:
ADJUSTMENT = [(RH-85)/10] * [(87-T)/5]
Heat Index
12. The Rothfusz regression is not appropriate when conditions of temperature and
humidity warrant a heat index value below about 80 degrees F. In those cases, a simpler
formula is applied to calculate values consistent with Steadman's results:
HI = 0.5 * {T + 61.0 + [(T-68.0)*1.2] + (RH*0.094)}
In practice, the simple formula is computed first and the result averaged with the
temperature. If this heat index value is 80 degrees F or higher, the full regression
equation along with any adjustment as described above is applied.
The Rothfusz regression is not valid for extreme temperature and relative humidity
conditions beyond the range of data considered by Steadman.
Heat Index
13. The maximum temperature percentile of a station refers to the ranking of the
maximum temperature of any particular day with respect to all the maximum
temperatures recorded for all the days of that months in record. For example, if
there were 100 maximum temperature value records and these are arranged in
ascending order, then the highest 90th value will be called 90th percentile, 95th
value will be called 95th percentile and 98th value will be termed as 98th
percentile. Statistically, the percentile values convey the information that 90th
percentile temperature indicate that the 90 percent of times the maximum
temperatures will be cooler than this temperature or in other words the maximum
temperature above 90th /95th/98th percentile indicate the unseasonably warm
day of any month.
By subtracting the temperature value from the 98th, 95th, and 90th percentile
marks, creating a departure map for the 98th, 95th, and 90th percentiles. This
applies to both the maximum and minimum temperatures.
Temperature Percentile Map & Departures
14. GIS based important Heat Wave Products (Completed)
Forecast Max Temp (up to 5
days)
Forecast Min Temp (up to 5
days)
Forecast Severe / Heat
Wave (up to 5 days)
Forecast Warm/very Warm
Night
90/95/98 Percentile of Max &
Min Temp
Forecast Temp, RH& Wind
Speed & direction
Forecast of Heat Index
Observed Max
Temperatures & Dep
Observed Min
Temperatures & Dep
Observed Severe/Heat
Wave
Observed Warm/Very
Warm Night
90/95/98 Percentile of
Max and Min Temp
Observed Relative
Humidity
Observed Temp, Wind
Speed & Direction
Observed Heat Index
12 UTC Today and Past 5days
03 UTC Today and Past 5days
12 UTC Today and Past 5days
12 UTC Today and Past 5days
03 & 12 UTC Today and Past 5days
03, 09 & 12 UTC Today and Past 5days
09 UTC Today and Past 5days
09 UTC Today and Past 5days
00 UTC MME for next 5days
00 UTC MME for next 5days
00 UTC MME for next 5days
00 UTC MME for next 5days
00 UTC MME for next 5days
09 UTC for next 5days
09 UTC for next 5days
15. The products are to be added in the heat wave GIS WEB Page
(Ongoing)
Climatology
Spatial Patterns of Maximum and Minimum normal for March – June
Heat Wave Days in March – June (1961-2020 or 1991-2020)
Average HW days during a) the El Nino years and b) La Nina years during the period
1961-2020
Monthly mean Relative Humidity (%)
Monthly mean Wind Speed (Knots)
Vulnerability due to heat wave 1969 to 2019
Vulnerable Zones due to heat wave (MAMJJ)
Monthly mean Hot Weather Hazard Scores
Heat Wave IBF
Heat Hazard Analysis
16. Thank you for your kind
attention.
Any queries or
suggestions
