Climate change analysis with monthly data (Clic-MD)

Abstract

The climate change is an issue of global concern in all areas of life, the global discourse has been well understood and disseminated; however, there is little understanding of the magnitude and direction of climate change locally. It is at this level where the mitigation and adaptation measures are taken, so is URGENT the knowledge through data of the current and local situation.
THE CLIC-MD SOFTWARE DEVELOPED IN UNAM FACILITATES:
1. The organization, storage and processing of millions of climate data (monthly temperature and precipitation).
2. The calculation more accurate of potential evapotranspiration.
3. The calculation of agroclimatic indices: humidity, aridity, erosion by rainwater, among others; improving agricultural activities and reducing damage to the environment.
4. The calculation of the continuous rainy season, which is vital to choose crop varieties, optimizing the rainwater uses (helping the conservation of aquifers) and achieves a greatest economic yield.
5. Identifying the trends of climate change at the local level (meaning and magnitude), which allows the prevention of adverse effects and harnessing the positive effects of this climate change.

Full text

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Climate change analysis with monthly data
(Clic-MD)
Concepts, equations and system use
Francisco Bautista1
Aristeo Pacheco2
Dorian Antonio Bautista-Hernández2
Febrero 2016
1
Centro de Investigaciones en Geografía Ambiental, Universidad Nacional Autónoma de México
2
Skiu, Scientific knowledge in use, www.actswithscience.com

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Bautista F., A. Pacheco., D.A. Bautista-Hernández. 2016. Climate change analysis with
monthly data (Clic-MD) Skiu. 57 pp.
ISBN: 978-607-96883-5-6
DR @ 2016. Skiu, Scientific Knowledge In Use ©
All rights reserved in accordance with the law. No part of this work may be reproduced by
any means, without written consent of Skiu or of the corresponding holders.
The authors are also grateful to Dr. Ma. Del Carmen Delgado Carranza and Eng. Oscar
Álvarez Arriaga.
This document was assessed by:
Dr. Oscar Frausto Martínez Universidad de Quintana Roo
Dr. Jorge L. Leirana Alcocer. Universidad Autónoma de Yucatán.
Dra. Elvira Díaz Pereira. Centro de Edafología y Biología Aplicada del Segura-Consejo
Superior de Investigaciones Científicas, Murcia, España.

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TABLE OF CONTENTS
1. INTRODUCTION ........................................................................................................................................ 6
2. VARIABLES INPUT ................................................................................................................................... 8
3. CLIC-MD INSTALLATION....................................................................................................................... 9
4. CLIC-MD SYSTEM OPERATION ...........................................................................................................12
4.1 CLIMATOLOGICAL STATIONS MENU ............................................................................................ 14
4.2 CAPTURE MENU ............................................................................................................................... 15
4.3 THE REVIEW MENU .......................................................................................................................... 18
4.4 EDIT MENU ......................................................................................................................................... 19
4.5 CALCULATION MENU ....................................................................................................................... 20
4.5.1 POTENTIAL EVAPOTRANSPIRATION .........................................................................................21
4.5.2. AGROCLIMATIC INDICES ...........................................................................................................25
4.5.3. CLIMOGRAM .................................................................................................................................28
4.5.4. LENGTH OF GROWING PERIOD (LPC) .....................................................................................31
4.5.5 MONTHLY RAINFAILL PROBABILITY .........................................................................................33
4.5.6. ANALYSIS OF TRENDS OF CLIMATE CHANGE ........................................................................36
4.5.7 IDENTIFICATION OF CLIMATIC ANOMALIES ..........................................................................45
4.5.8 GRAPHICS OF ANNUAL INCREASES AND DECREASES OF CLIMATIC ELEMENTS .............47
4.5.9 DESCRIPTIVE MONTHLY STATISTICS OF CLIMATIC ELEMENTS ..........................................49
4.5.10. CLIMATIC AND AGROCLIMATIC DATA SUMMARY ...............................................................50
5. OPTIONS MENU ........................................................................................................................................51
6. HELP MENU ...............................................................................................................................................52
6.1 ABOUT CLIC-MD ..............................................................................................................................52
APPENDIX I ....................................................................................................................................................55

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Index of Tables and Figures
Figure 1. Clic-MD input and output variables…………………………………... 7
Figure 2.a. Installation screen ……………………………………………………. 9
Figure 2.b. Default installation directory screen ……………………………. 10
Figure 2.c. Installation progress screen………………………………………….. 10
Figure 2.d. Installation completed screen………………………………………... 11
Figure 3.a. Select language to work with Clic-MD………………………............. 12
Figure 3.b. Clic-MD, startup screen……………………………………………….. 12
Figure 4. Clic-MD, main screen....................................................................... 13
Figure 4.1.a. Climatological Stations………………………………………………... 14
Figure 4.1.b. Enter a new climatological station…………………………………… 14
Figure 4.2.a. Data entry by years group……………………………………............. 16
Figure 4.2.b. Data entry by year……………………………………………………... 17
Figure 4.2.c. Select Excel data spreadsheet………………………………............. 18
Figure 4.3. Review of data to check don't overlapping …………………… 19
Figure 4.4. Edit data……………………………………………………………….. 20
Figure 4.5. Calculation menu…………………………………………..……..... 21
Figure 4.5.2. Agroclimatic indices calculation…………………………………….. 28
Figure 4.5.3.a. Climogram of rainfall and temperature………………………….. 29
Figure 4.5.3.b. Graph of monthly averages………….…………………………… 30
Figure 4.5.3.c. Monthly thermal amplitude ……………………………………….. 30
Figure 4.5.4. Length of growing period………………………………..………... 31
Figure 4.5.5.a. Graph of rainfall probability in a wet month ……………………. 34
Figure 4.5.5.b. Graph of rainfall probability in a dry month …………............. 35
Figure 4.5.6.a. Data set to analyze………………………………………………….. 39
Figure 4.5.6.b. Results with Mann Kendall test with annual data………………. 40
Figure 4.5.6.c. Results with Mann Kendall test with monthly data……………… 40
Figure 4.5.6.d. Z values in the Mann Kendall test………………………………. 41
Figure 4.5.6.e. Graph of the Mann Kendall test …………………………………… 42
Figure 4.5.6.f. Linear correlation of monthly climatic elements………………… 43
Figure 4.5.6.g. Linear correlation with annual data of agroclimatic indices and

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climatic elements………………………………………………………………. 44
Figure 4.5.7.a. Temperature anomalies and extreme events…………………….. 45
Figure 4.5.7.b. Normal distribution of two periods of maximum temperature (May)
…………………………………………………………………………………………… 45
Figure 4.5.8.a. Graph of increases and decreases relative to average; maximum
temperature of April in Progreso, Yucatán…………………………………. 48
Figure 4.5.8.b. Graph of increases and decreases relative to average; September
rainfall in Peto, Yucatán………………………………………………………. 48
Figure 4.5.9. Descriptive statistics table of climate elements by month…………. 48
Figure 4.5.10.a. Monthly averages of the elements of weather and annual
agroclimatic indices ……………………………………………………………. 49
Figure 4.5.10.b. Summary of the monthly climate change trends ……………. 50
Figure 5. Menu Options…………………………………………………............. 50
Figure 6. About Clic-MD…………………………………………………………... 51

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1. INTRODUCTION
The software Clic-MD facilitates handling large amounts of data of climate
elements, creating graphs to display thousands of data in seconds.
The computer system Clic-MD allows organize, store and handle of climate data
used for Evapotranspiration (ET0) analysis and of different Agroclimatic indices.
The database can be enriched from different sources, including the global climate
database ERICK III.
The climatic elements and climate indices stored in Clic-MD are those commonly
measured in any climatological station in the world, this allows estimating ET0 with
empirical tests most used: Hargreaves and Thornthwaite.
Unlike other programs that perform the calculation of ET0 with Hargreaves and
Thornthwaite Tests, Clic-MD allows changes in the constants of these equations or
methods with the aim of using the values in accordance to the calibration with the
reference method (ET0-PM). This allows getting the best estimates of ET0.
Clic-MD (Figure 1.) can be very useful to…:
a) To store in an orderly way, thousands of climate data from georeferenced
climatological stations.
b) To check the consistency of the data with the minimum temperature, average
and maximum.
c) To correct wrong data
d) Very fast queries about climate elements stored (menus, windows, and icons for
easy use).
e) To calculate evapotranspiration and agroclimatic indices; making climograms
and graphs of length of growing period and rainfall probability, and descriptive
statistics of climate elements. Making it possible to improve agricultural activities
and reduce environmental damage. Clic-MD allows knowing continuous rainy

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season, essential to choose crop varieties, optimizing the rainwater use, helping
the conservation of aquifers and achieve greatest economic yield.
f) Calculation of climate change trends and climate anomalies and analysis of
extreme weather events, helping to decision makers to take advantage of the
positive effects of climate change.
Figure 1. Clic-MD input and output variables

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2. VARIABLES INPUT
The weather observation
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recorded represents the primary focus of the information
system. Variables input have been selected according to the values used for the
calculation of ET0 by Hargreaves and Thornthwaite tests.
The weather station is identified by the following information:
 Station code or Ref, using three letters to the states and two or three
numbers for municipalities is recommended.
 Latitude: in degrees, minutes and seconds.
 Longitude: in degrees, minutes and seconds.
 Altitude: in meters.
Stored monthly data refer to the following variables:
 Maximum temperature, in °C.
 Average temperature, in °C.
 Minimum temperature, in °C.
 Precipitation, in mm.
It is very important to check the correct data of latitude and longitude because
based on the geographical location Clic-MD calculates extraterrestrial solar
radiation (Ra) and sunshine hours, both necessary for the calculation of ET0.
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The weather observation is performed in weather stations thereby generating historical data that
they allow the study of climate. The meteorological stations can also be called climatological
stations by the historical records; however, the meteorological term is more appropriate because
they are recorded the weather, which then allows the climate analysis.

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3. Clic-MD INSTALLATION
The software Clic-MD will be provided on a distribution CD that contains the
installer program: setup.exe file, which will install the application and the necessary
files for operation on your computer. To do this insert the CD and run setup.exe,
follow the instructions on the screen (Figures 2.a.b.c.d.).
Then the database and system will remain in the directory:
C:\ Program files\Clic-MD
You can change the directory, but we recommend leaving the default directory.
After the installation, a shortcut icon to Clic-MD on the desktop will be found.
Figure 2.a. Installation screen

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Figure 2.b. Default installation directory screen
Figure 2.c. Installation progress screen

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Figure 2.d. Installation completed screen

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4. CLIC-MD SYSTEM OPERATION
The Clic-MD system is presented in English and Spanish, language will be
selected to start the application by clicking on the drop down list (Figure 3.a.). After
selecting the language the startup screen Clic-MD is displayed in selected
language (Figure 3.b.).
Figure 3.a. Select language to work with Clic-MD
Figure 3.b. Clic-MD startup screen

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The Clic-MD system is user-friendly, providing a graphical environment through a
set of screens and windows with bars and icons.
The screens have several bars and icons. On the main screen you can see: the
menu bar (1) and toolbar (2), the first one with menus: stations, capture, review,
modify, calculations, options and help (Figure 4.).
The second bar icons are initially disabled, but when choosing an option from the
menu bar, are activated according to the open option, they are:
1. New. Allows users to create a new climatological station.
2. Save. Saves all changes made.
3.- Save and New. Allows users to save an existing configuration and then
create a new station or configuration.
4. Modify. Allows changing the selected climatological station.
5. Delete. Allows users to delete the station or selected data.
6. Copy. Copy the selected content.
7. Paste. Paste previously copied information.
8 Recalculation. Allows users to perform a new calculation of ET0.
9. Exit. Exits from Clic-MD program.
Figure 4. Clic-MD main screen
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1

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4.1 CLIMATOLOGICAL STATIONS MENU
In this menu, all climatological Stations that are in the database Clic-MD system in
tabular form (Figure 4.1.a.) are shown. The information displayed for each station
is: Code or Ref, Name, Latitude, Longitude, Altitude, Country and State.
When the "Stations" menu is selected, the "New" icon in toolbar is activated, this
icon opens a new window (New station) in which you can enter a new
climatological station with all their individual data (Figure 4.1.b). The menu bar
includes the ability to edit and delete climatological stations.
Figure 4.1.a. Climatological stations
Figure 4.1.b. New climatological station

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4.1.1. NEW CLIMATOLOGICAL STATION (Figure 4.1.b.)
Fields to enter a new climatological station are:
 Ref: Code or Reference of climatological station. Limited to 10 characters.
 Name: Name of climatological station. Limited to 100 characters.
 Country and State.
 Latitude: Latitude of climatological station. Field with data input format, one
Letter (N for North or S for South) and 6 Digits: LDDDDDD.
 Longitude: Longitude of the climatological station. Field with data input
format, one Letter (E for East or W for West) and 6 or 7 Digits: LDDDDDD or
LDDDDDDD. (Example: N666666, W666666).
 Altitude: Altitude of climatological station. Limited to 4 digits.
With Clic-MD is possible to verify the geographical position of the climatological
stations, the extraterrestrial radiation and sunshine hours are calculated from these
important data, both essential for evapotranspiration calculation.
Internet access is required.
4.2 CAPTURE MENU
In the Capture menu first select the climatological station in which will upload the
data. By double-clicking on the name of the station to select the climatological
station or seek the station by: reference, name, altitude, or state. The data will be
loaded and shown in the "station data" box inside of the window "Data entry".
To proceed to introduce the data of temperature and precipitation of a group of
years or one year in particular click on the Configure button to open the boxes on
the screen according to the defined period of study (Figures 4.2.a.). Similarly, you
can load data from a single year and in another format as shown in Figure 4.2.b.
Data are loaded by copying the source file from Excel to Clic-MD just by clicking

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the paste button. You must first select the data set in Excel (Figure 4.2.c.), then
select the first cell in the table and then click the Paste icon.
Figure 4.2.a. Capture by years group
If you make a selection mistake of climatological station or entry data is possible to
clean or delete that data.
Once entered data, click the "Save" icon to update the database. If any data
has not been captured, the system automatically places the value 999.99 which
refers to data that were not included and, therefore, not be taken into account in
the calculation of ET0 or indices.

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For missing data the system can calculate an average considering data from five
years before and five years later (Orellana, 2011), these estimates data are
marked with yellow in order to remember that it is estimated data.
Figure 4.2.b. Data entry by year

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Figure 4.2.c. Select data from Excel spreadsheet. Warning! Make sure the data set
is selected properly.
4.3 THE REVIEW MENU
First the climatological station to review is selected, and then the data of maximum
temperature, average and minimum by month are displayed. With the display
button the data are displayed in a table or a graph to facilitate the identification of
errors in data (Figure 4.3.); checking overlapping values: the minimum
temperatures must be below in the graph and the values of maximum
temperatures will be above.
You can export the graph as PDF or send it by e-mail.

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Figure 4.3. Checking overlapping data
4.4 EDIT MENU
This menu is used when a minimum temperature data is greater than the average
or maximum, or when there is another kind of inconsistency as extreme data that
clearly fall outside the pattern and of the normal observed intervals, for example,
data from three digits or greater than 60 degrees.
You can select the climatological station and the period in which you will be making
changes in data, so the data are displayed in the cells and you can to modify them
(Figure 4.4.).

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Figure 4.4. Editing data
4.5 CALCULATION MENU
The calculation menu is the base of system; it is possible to calculate
evapotranspiration, agroclimatic indices, climograms, changing trends, anomalies,
length of growing period, rain probability, increases and decreases in annual
temperatures and descriptive statistics (Figure 4.5.).
Select the climatological station and the period for calculation.

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Figure 4.5. Calculation menu
4.5.1 POTENTIAL EVAPOTRANSPIRATION
Information on evapotranspiration (ET0) and consumptive water use are important
for the planning of water resources for irrigation scheduling on crop and forestry.
Evapotranspiration is also very important to understand how natural plant
communities work; how changes of vegetal cover of land modify the ET0 and the
energy balance.
The knowledge and measuring changes on ET0 are needed to understand
ecohydrological changes (Bautista et al., 2009).

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Potential evapotranspiration is calculated based on atmospheric forces and the
various types of surface. In order to eliminate the influence of surface types, the
concept of reference evapotranspiration (ET0) was introduced to study the
evaporative power of the atmosphere regardless of type, development and
handling practices of crop (Allen et al., 1998).
This climatic parameter (ET0) represents the evapotranspiration of a standard area
of vegetation, considering that available water is in abundance in the area of
reference evapotranspiration, then soil factors do not affect the ET0. In general, the
techniques for estimating ET0 are based on one or more weather variables or in
some measurements related to these variables as the "evaporation of try".
Some of these tests are accurate and reliable; others offer only an approximation.
4.5.1.1 THE POTENTIAL EVAPOTRANSPIRATION ESTIMATED BY
THORNTHWAITE TEST
The empirical calculation of potential evapotranspiration using the Thornthwaite
model (1948) (ET0(T)) is basically done using the average temperature, but also
includes a correction factor for the length of day in function of the latitude.
According Llorente (1961), the calculation is carried out with the following formula:



 


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





Where
N = Maximum number of sunshine hours, depending on the month and latitude
ET0sc= Uncorrected potential evapotranspiration
dm = number of days per month
C = 16, a constant
I = annual heat index
i = monthly heat index
a = exponent depending on annual index
tmed = average temperature by month
Clic-MD calculates the ET0(T) in daily average for month, monthly average for a
year, and annual average for the selected period of the years.

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4.5.1.2 THE POTENTIAL EVAPOTRANSPIRATION ESTIMATED BY
HARGREAVES TEST (1985)
The empirical calculation of evapotranspiration potential using the Hargreaves test
is performed as follows:

Where:
Ci= 0.0023, a constant
tmed = medium or average temperature
tmax = maximum temperature
tmin = minimum temperature


Where:
 = extraterrestrial radiation according to latitude
 = Pi
 = Solar constant (0.082 MJm-2min-1)
= Inverse relative distance Earth-Sun
 = angle at sunset
 = latitude (rad)
 = Solar declination
In grid shown the observed station data and additional data for calculating ET0,
these values are (Figure 4.5.): Year, month, maximum temperature, average
temperature, minimum temperature, precipitation, solar radiation (see formula for
Ra in output variables), sunshine hours (See formula for N in Concepts), ET0 by
Hargreaves and Thornthwaite in -mm/day and -mm/month-. These values are
calculated.

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The default monthly values are shown in box "Constants" of constants of the
equations of Hargreaves and Thornthwaite for calculating ET0; these values can be
changed in each field according to user needs (Bautista et al., 2009).
For the estimation of ET0 is previously calculated the extraterrestrial radiation (Ra)
and sunshine hours using the geographical position of the weather station.
4.5.2. AGROCLIMATIC INDICES
4.5.2.1. HUMIDITY INDEX (HUi)
The annual index is used to estimate, in a general way, the available water by
plants. It is also often used to anticipate the needs of artificial drainage in an area,
or to classify the months and years depending on the humidity of the site and thus
account for the intra-annual humidity of a place, similar to the length of the period
of growth (FAO, 1996) or the length of the rainy season (Delgado, 2010).
To calculate the humidity index (HUi) the following formula is applied:
 

Where:
P = precipitation
ET0 = potential evapotranspiration (by Thornthwaite or Hargreaves test)
The value of this index ranges from <0.05 to >2, with eight categories: Hyper-arid
<=0.05, arid >= 0.05 - <= 0.2, semi-arid >=0.2 - <=0.5, dry sub-humid >=0.5 -
<=0.65, humid sub-humid >=0.65 - <=1, humid >=1 <=1.5, very humid >=1.5 - <=2
and hyper-humid >2 (Lobo et al., 2004).

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4.5.2.2. ARIDITY INDEX (ARi)
As an annual index, this simple procedure attempts to estimate the general aridity
of the climate. The aridity index (ARi) is calculated based on the number of months
of the year when potential evapotranspiration (calculated by Thornthwaite or
Hargreaves test) exceeds precipitation.
4.5.2.3. VEGETATIVE DEVELOPMENT PERIOD (GS)
It is a simple procedure for calculating the length of vegetative growing season
(GS), estimated by the number of months of the year when the average
temperature exceeds 5 °C (CEC, 1992), situation very important in temperate and
cold regions.
4.5.2.4. PRECIPITATION CONCENTRATION INDEX (PCi)
In order to estimate the aggressiveness of the rains, from the temporal variability of
monthly precipitation, Oliver (1980) proposed the precipitation concentration index
(PCi), expressed as % (percentage), by the following formula:


Where:
p = monthly precipitation
P = annual precipitation
This index, whose value ranges between 8.3 and 100%, seems an appropriate
statistical expression to compare the concentration of rainfall between seasons.
Thus, a low index value indicates a uniform distribution of rainfall, while a high
index value indicates a high concentration of it.

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4.5.2.5. MODIFIED FOURNIER INDEX (MFi)
The modified Fournier index (MFi) is frequently used for estimate rainfall erosivity
(R factor) in the process of soil erosion. As an annual index is defined by Arnoldus
(1980) according to the following expression:


Where:
 = monthly precipitation
P = annual precipitation
MFi intervals are: 0-60, 60-90, 90-120, 120-160 and over 160, corresponding to the
categories of very low, low, moderate, high and very high, respectively (CEC,
1992). Despite their frequent general use, this index appears only valid and
applicable within a same climatic region, i.e. homogeneous climatic regions which
should be considered independently.
4.5.2.6. ARKLEY’S INDEX (AKi)
The Arkley index (AKi) is used to estimate the effect of climate on the process of
soil leaching. Arkley (1963) defined this annual index as the highest value of the
sum of the monthly precipitations minus the potential evapotranspiration value
(calculated by Thornthwaite test or Hargreaves test) of those months where
precipitation exceeds evapotranspiration, or the total amount of precipitation of
wetter month.
With Clic-MD is possible to calculate the agroclimatic indices by year and for period
of years of interest. Agroclimatic indices can be calculated using the potential

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evapotranspiration calculated either with the Hargreaves or the Thornthwaite test
(Figure 4.5.2).
You can also create graphs with the monthly averages of agroclimatic indices
The data can be exported from excel or txt format.
Figure 4.5.2 Agroclimatic indices calculation
4.5.3. CLIMOGRAM
The climogram is a graphical representation of the average monthly rainfall in mm
(y-axis) and the average monthly temperature in degrees Celsius (y’-axis). The
peculiarity is that the axis of precipitation is twice the average monthly temperature

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because it attempts to show you the dry and wet months (Figure 4.5.3.a.),
according to Gaussen aridity index:
Precipitations in mm = Temperatures in °C x 2
Thus, if the value of the precipitation is less than twice the average temperature,
the month is dry while the month will be wet when the precipitation is higher than
the temperature.
We recommend you use an average of 30 years to know about the climate of a
locality or shorter periods when you want to study changing trends.
With Clic-MD, on the tab "monthly averages" are calculated monthly averages of
climate elements (maximum temperatures, average and minimum as well as
precipitation) and evapotranspiration, can be displayed as a data table or graph
(Figure 4.5.3.b.).
You can select the period of years of interest and export graphics in different
formats or send it by e-mail if you have Internet access. In this section, you can
calculate also the monthly thermal amplitude (the difference between maximum
temperature and the minimum temperature) (Figure 4.5.3.c.). You have the option
to graph and calculate the linear regression to observe changes in this climate
parameter.

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Figure 4.5.3.a. Climogram of rainfall and temperature

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Figure 4.5.3.b. Graph of monthly averages
Figure 4.5.3.c. Monthly thermal amplitude
4.5.4. LENGTH OF GROWING PERIOD (LPC)
The agroecological zone is a concept that includes and integrates the climate in
agricultural aspects by another concept, which is the length of the growing period
(LPC) is the period of the year when the humidity and temperature are suitable for
the production crop, i.e. is the time of year of continuous rain and sufficient for
agriculture (Delgado, 2010).
The estimation of LPC is performed considering the water balance model, by the
ratio of rainfall (P) with potential evapotranspiration (Et0). If the LPC is not limited
by temperature (> 6.5 ºC), the P/Et0 relation determines the type of LPC, when it
starts? how long it lasts? and when it ends? Its ranges from the day when
precipitation exceeds half the ET0, until the day when amount of rainfall is less than
half the ET0. It also influences the type of soil and its moisture retention capacity.

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The LPC provides an ideal framework to summarize the inter-annual behavior of
the climate, since you can compare the requirements and estimated responses of
plants (Delgado, 2010).
The temperature regime, precipitation (P), evapotranspiration and incidence to the
extreme weather events, are more relevant when calculated for the LPC, when
they can influence the development of the crop, than if it done for the annual
average (FAO, 1996).
With Clic-MD the precipitation and total monthly evapotranspiration and half of that
value is graphed, whereby the dry months are identified (less rainfall than half of
ET0), wet months (higher rainfall that half of ET0) and the wetter period (greater
rainfall than ET0). The graph can be drawn the rainfall in lines or bars (Figure
4.5.4).
Like another products, the graph can be exported or sent by e-mail. The data can
be displayed with the "show" button and can be exported in Excel and txt format.

33
Figure 4.5.4. Length of growing period
4.5.5 MONTHLY RAINFAILL PROBABILITY
The Gamma function is the probability model used for the analysis of historical
monthly precipitation data. Adjusting the Gamma function to monthly precipitation
records is based on the calculation of the parameters that shape the function.
First you need to calculate an auxiliary variable A:




34
Where:
ln X = Natural logarithm of the average of the data
N = amount of data
= Sum of the natural logarithms of the data
Later with this variable A, is possible calculate the two variables that will shape to
the probability function adjusted to the values for each month,  = alpha and  =
beta:


 

Once obtained the values of parameters alpha and beta, the calculation of the
gamma probability function can be done.



Thus, the area under the curve of this function, calculated with its corresponding
integral, represents the probability to find a less or equal value to this one, i.e. the
limit value to the right used as reference. For precipitation analysis we need the
probability of finding a higher or equal precipitation to each value, so it is necessary
to calculate the complement those previously obtained simply by subtracting 1 to
each value.

35
With Clic-MD the curve of accumulated precipitation by month is quickly and
automatically calculated and in two periods, this allows inferring climate change
between a reference period and the period to assess. It is recommended that the
period to compare must be at least of 20 years. Note the change of the curve in a
wet month (Figure 4.5.5.a.) and a dry month (Figure 4.5.5.b.) Data are displayed
when clicking on the button "show". You can export the graph as PDF or send by
e-mail
Figure 4.5.5.a. Graph of rainfall probability in a wet month

36
.
Figure 4.5.5.b. Graph of rainfall probability in a dry month
4.5.6. ANALYSIS OF TRENDS OF CLIMATE CHANGE
4.5.6.1 CORRELATION COEFFICIENT BY MANN-KENDALL
The Mann Kendall Test (MK-T) is a nonparametric statistical test; used to identify
nonlinear trends of a data series at equal time intervals, in this case, of the
elements of climate and agroclimatic indices that shown "non normal" distribution
type.
The procedure of the MK test begins by simply comparing the most recent data of
the time series with previous values. A score of 1 is given if the latest concentration

37
is larger, or a score of -1 if is smaller. The total score for the data series is the MK
statistic, which is compared to a critical value to verify if data show a trend of
change, and if yes, if this is an increasing or a decreasing trend (Carlón and
Mendoza, 2007; Castañeda and González, 2008).
The process for the analysis is in the following way:
1. The n data pairs (x1,y1), (x2,y2),…(xn,yn) are indexed according to the
magnitude of the value of x, such that x1≤ x2≤… ≤ xn and yi is the value of
the dependent variable corresponding to xi.
2. Examine all n(n-1)/2 ordered pairs of yi values. Let P be the number of
cases where yi>yj(i>j), and let M be the number of cases where yi<yj(i>j).
3. Define the test statistics S= P-M
4. For n>10, the test is conducted using a normal approximation. The
standardized test statistic Z is calculated:













5. The null hypothesis is rejected at significance level α if (|Z|>Z(1-α)/2, where
Z(1-α)/2 is the value of the standard normal distribution with a probability of
exceedance of α/2. For example, if α = 0.05, then the null hypothesis would
be rejected for |Z|> 1.96. In cases where some of the x and/or y values are
tied, this formula for Var(S) is modified.
If the sample size is less than 10, then it is necessary to use tables for the S
statistic.

38
6. The Kendall correlation coefficient τ is defined as:
 


As with other types of correlation coefficients, τ can only take values between -1
and 1, its sign indicating the sign of the slope of the relationship, and the absolute
value indicating the strength of the relationship.
Because the test is based only on the rows of data, it can be used even in cases
where some of the data are disapproved. This is an important feature of this test
for its application in climatology. When there are missing values in a data set, then
it introduces a correction in the formula for the variance of S so that all of missing
values will be added; the formula is:




Where ti is the number of links of extent i.
The test cannot be employed when there are multiple rejection thresholds in data
set of the null hypothesis because the values cannot be classified unambiguously
(Hirsch et al., 1993).
In this case, the characteristics of the MK test are: a) The test does not take into
account the magnitude of the data; b) The MK test is less sensitive to extreme
data; c) The test does not take into account the temporal variation in the data so
that we cannot obtain the magnitude of the trend, and d) Data should be free of
"seasonality". When data are seasonal we recommend using extreme
temperatures rather than averages. A "no trend" result is not equivalent to a stable
data, is equivalent to a trend not detected by this test. A result of "decreasing" or

39
"increasing" trend is a stronger conclusion than a result "no trend". A lesser
amount of available data lower reliability test MK.
With Clic-MD, the climate elements and /or agroclimatic indices to which the MK
trend test is to be applied are selected; the results of the test are showed on the
screen with the parameters S, Var, N and Zstd, respectively corresponding to:
trend statistics, variance, number of cases in the series of data, and the
standardized Z value.
.
If Z > 1.96, the data series are statistically significant, in other words, a trend exists.
A positive value of Z indicates an upward trend; a negative value indicates a
downward trend in the data series.
With software Clic-MD the identification of trend to climate change is performed
with this statistical test (MK) by following these steps:
First the climatological station under study and the period of interest are selected.
Calculations are performed. Then we can calculate the climate change trends with
annual and/or monthly data. The results are shown in tabular form.
To identify trends of annual climate change the agroclimatic indices and weather
elements are used. You can select the period of years of interest.
To identify trends of monthly climate change, the temperature (maximum, medium
and minimum) and precipitation are used.
The data can be exported to excel or txt.
It is possible to graph the monthly data with the value of Z of MK test.
The options are: Data, Annual MK, Monthly MK, dataset MK, Station MK and
correlations.

40
The Data option corresponds to the monthly data shown for years (Figure 4.5.6.a.).
The temperature data by month of each year are shown, as well as the monthly
maximum value, minimum, and average by year are displayed by rows;
furthermore also shown by columns, the maximum value, minimum and average
data by each month for all years.
The data are displayed according to the parameters of the selection box: Maximum
Temperature, Average Temperature, Minimum Temperature and Precipitation.
Figure 4.5.6.a. Data set to analyze

41
In the "Annual Mann Kendall" framework you can select the period of interest, with
Mann Kendall test the value of agroclimatic indices, temperature, precipitation and
potential evapotranspiration is calculated (Figure 4.5.6.b.).
Figure 4.5.6.b. Results with Mann Kendall test with annual data
Figure 4.5.6.c. Results with Mann Kendall test with monthly data

42
In the "Mann Kendall Monthly" tab, in the sidebar "Months" you can select the
months for which you want to calculate the statistical test of Mann Kendall by
clicking aside to the desired month or months. In this screen shows data
"Parameters" you can select the variables to analyze: temperatures and/or
precipitation. The calculated data will be displayed in a table on this tab (Figure
4.5.6.c.).
To facilitate interpretation of result with this test, when an increasing trend of
climate element or studied index is detected, the box turns red; or if decreasing
trend is detected, it is colored blue; and remains white when there is no trend of
change.
The results of "Z" from the MK test can be graphed. Clic-MD provides two options:
per station or group of stations. By station: click on the Calculations menu and
select submenus: Monthly calculations / Trends / Station Mann Kendall by set of
stations: follow the same route, just at the end choose Mann Kendall set in addition
select by clicking the checkbox TSMK the stations to apply the test. Click on "show
data" and the table displays data (Figure 4.5.6.d.).
Figure 4.5.6.d. Z values in the Mann Kendall test

43
Select from "Data" the climate element to obtain a graph (temperature or
precipitation), select the stations again, click on right and choose the option
"Graph" (Figure 4.5.6.e.).
Figure 4.5.6.e. Graph of the Mann Kendall test
4.5.6.2 PEARSON'S CORRELATION COEFFICIENT
The correlation coefficient, expressed by a number between -1 and 1, measures
the degree of linear relationship between two variables. Will be a positive number
when the slope also be positive, that means, a relationship directly proportional
and a negative value when an inverse relationship. Correlation is classified as
follows:
+1 or -1= Perfect correlation; 90%= Very high correlation; 80%= High correlation;
70%= Good correlation; 50%= Partial correlation; 0%= No correlation.

44
Correlation analysis can be used as an initial approach to identifying changes in
the climatic elements and in the agroclimatic indices. It can be used despite that
the time series may contain discontinuous data.
The linear correlation coefficient is a way to identify or detect trends of change with
increments in the elements of climate and in agroclimatic indices (Figures 4.5.6.f. -
g).
Clicking on the desired month, Clic-MD performs the linear correlation analysis and
the result is shown graphically; within seconds the graph is obtained, draws the
line, and calculates the equation as well as r and r2 of that month. This is possible
by clicking on the show button. You can also export the graph or send it by e-mail.
Figure 4.5.6.f. Linear regressions of monthly climatic elements

45
Figure 4.5.6.g. Linear regressions with annual data of agroclimatic indices and
climatic elements
4.5.7 IDENTIFICATION OF CLIMATIC ANOMALIES
Temperature anomalies are the differences between the average temperature of
the year in question (or any period of years) and a reference period considered
normal (Figure 4.5.7.a.). Commonly in studies of climate change is considered as
the reference period prior to 1990, such as 1950-1990. The period or year to
compare must be after 1990. However, several authors may consider different
periods of reference and comparison, such as 1961-1990 and 1961-2005 like
reference periods and 1986-2005 like period to compared (IPCC, 2001; IPCC,
2013).

46
Figure 4.5.7.a. Temperature anomalies and extreme events
Extreme periods or events are those with very high or very low values of climatic
elements, with a probability of occurrence of 0.01 (Beniston, 2008) to 0.05 (Figure
4.5.7.a); that is, those values that are above 95% to 99% of the data set both
upward and downward, which can be identified with the normal distribution of data.
Identifying climate anomalies corresponding to the ends of the normal distribution
curve is used to identify the values above 95% or below 5%. In the graph these
ends of the curve are highlighted in green (Figure 4.5.7.b.).
Figure 4.5.7.b. Normal distribution of two periods of maximum temperature (May)

47
The parameters used in the graphs of normal distribution are: maximum, average
and minimum temperature. You can select them by month. The two periods to
comparing are determined as appropriate in sidebar "Select periods" (Figure
4.5.7.b.). The graph automatically switches to select a different month and / or
temperature. The analysis data are displayed by clicking the "Show" button. The
graph can be exported to PDF or send it by e-mail.
The graph in this Figure aims to visually compare two time periods, which could be
the year of origin of the data, such as 1961-1989 and 1990 to present.
4.5.8 GRAPHICS OF ANNUAL INCREASES AND DECREASES OF
CLIMATIC ELEMENTS
The graphs of increases and decreases are a way to show the annual anomalies of
climatic elements. Sometimes with these graphs it is possible to identify the
magnitude of climate change in recent years such as in the graph of Figure 4.5.8.a.
increases in the maximum temperature is observed during April from 1997 to 2006
at the meteorological station of Puerto Progreso Yucatan.
When working with rainfall data can be identified dry years or periods as well as
the presence of hurricanes, as shown in Figure 4.5.8.b.
Data can be displayed by clicking the “Show” button and can also be exported in
PDF format or send it by e-mail.

48
Figure 4.5.8.a. Graph of increases and decreases of temperature with respect to
average; maximum temperature of April in Progreso, Yucatán.
Figure 4.5.8.b. Graph of increases and decreases of precipitation with respect to
average; rainfall of September in Peto, Yucatán.

49
4.5.9 DESCRIPTIVE MONTHLY STATISTICS OF CLIMATIC
ELEMENTS
Finally with Clic-MD is possible to get data descriptive statistics of climate elements
by month, these data are displayed in seconds by clicking on the month you wish
to observe.
The descriptive statistic includes maximum temperature, average and minimum as
well as precipitation and potential evapotranspiration.
You can select the period of data that you want. The data table can be exported to
Excel or txt (Figure 4.5.9).
Figure 4.5.9. Table of descriptive statistic climate elements by month

50
4.5.10. CLIMATIC AND AGROCLIMATIC DATA SUMMARY
With Clic-MD we can deploy two tables. The first is relative to the monthly
averages of the elements of weather and annual agroclimatic indices (Figure
4.5.10.a.) and the second one is about the summary of the monthly of climate
change trends using the Mann Kendall test of the climate elements (Figure
4.5.10.b.).
When the purpose of using Clic-MD is the knowledge of climate change trends, it is
recommended to start with the summary data to know if there is a changing trend.
Once found the months for change is recommended to proceed with the graphics
of increases and decreases to identify the reference period and the period of
change, so continue with the analysis of anomalies using both periods (baseline
and the change).
Figure 4.5.10.a. Monthly averages of the elements of weather and annual
agroclimatic indices

51
Figure 4.5.10.b. Summary of the monthly climate change trends
5. OPTIONS MENU
The displayed options are three:
 Language (change from Spanish to English or vice versa)
 Backup (makes a backup of the database)
 Clean (clean or delete the database) (Figure 5).
Figure 5. Menu Options

52
6. HELP MENU
6.1 ABOUT CLIC-MD
This submenu displays information about the system: name, version, copyright,
company description, etc. (Figure 6).
Figure 6. About Clic-MD

53
7. REFERENCES
Allen, R. G., Jensen, M. E., Wright, J. L., & Burman, R. D. 1998. Operational
estimate of reference evapotranspiration. Agronomy Journal, 81, 650-662.
Arkley, R. 1963. Relationships between plant growth and transpiration. Hilgardia
34:559-584.
Arnoldus, H.M.J. 1980. An approximation of the rainfall factor in the universal soil
loss equation. In: M. de Boodt and D. Grabriels (eds.), Assessment of
erosion. John Wiley & Sons, Inc., New York.
Bautista F, Bautista D y Delgado-Carranza C. 2009. Calibration of the equations of
Hargreaves and Thornthwaite to estimate the potential evapotranspiration in
semi-arid and subhumid tropical climates for regional applications. Atmósfera.
22(4): 331-348.
Beniston, M. 2008. Extreme climatic events and their impacts: examples from the
Swiss Alps. En H. F. Díaz, & R. J. Murnane, Climate extremes and society.
Cambridge University Press, pp 147-164. New York.
Borges A. C. y E. M. Mendiondo, 2007. Comparação entre equações empíricas
para estimativa da evapotranspiração de referência na Bacia do Rio
Jacupiranga. Revista Brasileira de Engenharia Agrícola e Ambiental. 11(3),
293–300.
Camargo A. P. y M. B. P. Camargo, 2000. Uma revisão analítica da
evapotranspiração potencial. Bragantia Campinas. 59(2), 125-137.
Carlón T. y M. Mendoza. 2007. Análisis hidrometeorológico de las estaciones de la
cuenca del Lago de Cuitzeo. Investigaciones Geográficas. 63: 56-76.
Castañeda M. y M. González. 2008. Statistical analysis of the precipitation trends
in the Patagonia region in southern South America. Atmósfera. 21: 303-317.
CEC, 1992. CORINE soil erosion risks and important land resources. Commission
of the European Communities, DGXII. EUR 13233 EN. Brussels.
Delgado Carranza C. 2010. Zonificación agroecológica del estado de Yucatán con
base en índices agroclimáticos y calidad agrícola del agua subterránea.
Tesis de Doctorado. Centro de Investigación Científica de Yucatán.

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FAO (Food and Agriculture Organization). 1996. Agro-ecological zoning:
Guidelines. FAO soils. Soil Resources, Management and Conservation
Service. FAO Land and Water Development Division. Bulletin 73. Rome,
Italy. 78 p.
Hargreaves, G.H. y Z. A. Samani, 1985. Reference crop evapotranspiration from
temperature. Appl. Eng. Agric. 1 (2), 96–99.
Hirsch R., D. Heisel, T. Cohn y E. Gilroy. 1993. Statistical analysis of hidrology
data. In: Handbook of hidrology. D. Maidment (Ed). McGraw-Hill Inc. USA.
IPCC. 2001. Climate Change 2001, The Scientific Basis. Contribution of
WorkingGroup I to the Third Scientific Assessment Report of the
Intergovernmental Panel on Climate Change: Cambridge, England,
Cambridge University Press.
IPCC, 2013, Climate change, bases físicas. Unidad de apoyo técnico del Grupo de
trabajo I del IPCC. OMM, PNUMA.
Lobo D., D. Gabriels, F. Ovalles, F. Santibañez, M. C. Moyano, R. Aguilera, R.
Pizarro, C. Sanguesa y N. Urra. 2004. Guía metodológica para la elaboración
del mapa de zonas áridas, semiáridas y subhúmedas secas de América
Latina y el Caribe. CAZALAC- PHI/UNESCO. Caracas, Venezuela.
Llorente, J.M. 1961. Meteorología. Editorial Labor. Barcelona, España.
Oliver, J.E. 1980. Monthly precipitation distribution: A comparative index.
Professional Geographer. 32:300-309.
Orellana, R., Hernández, M. E. & Espadas, C. 2011. Ambiente. Clima. En F.
Bautista, Técnicas de muestreo para el manejo de Recursos Naturales.
Segunda Edición, pp 189-225. México, DF.
Thornthwaite C.W. 1948. An approach toward a rational classification of climate.
Geogr. Rev. 38, 55-94.
Willmott C. J., 1982. Some comments on the evaluation of model performance.
Bull. Am. Meteorol. Soc. AMS. 63 (11): 1309–1313.

55
APPENDIX I
TECHNICAL DATA
II.1 COMPUTER REQUIREMENTS
 CPU: 1.0 GHz or higher processor
 RAM: 256 Mb for an optimal performance.
 Screen: VGA for graphical representations. Recommended resolution of
1200x800
 Optical unit: CD-ROM for installation
 Hard Drive: enough free space for program and data. 50 Mb free for system
installation and data.
 Java Virtual Machine V1.6(JVM)
 Operating System: Microsoft Windows XP, Windows Vista, Windows 7 or
releases above XP; Linux, any version that supports Java Virtual Machine;
Mac, any version that supports Java Virtual Machine.
II.2 SYSTEM FILES
Directory \MOCLIC\
MoclicM.jar
DBMOCLICM
Icons, Logos, Icon1.icon, Unins000.dat, Unins000.exe
II. 3 POSSIBLE FAILURES
Frequent failures in installation are due to insufficient disk space or to the versions
of the operating system and installed packages.
Problems may arise during execution of the application when making calculations
due to errors in entered data.

56
The climate change is an issue of global concern in all areas of life, the global
discourse has been well understood and disseminated; however, there is little
understanding of the magnitude and direction of climate change locally. It is at this
level where the mitigation and adaptation measures are taken, so is URGENT the
knowledge through data of the current and local situation.
THE CLIC-MD SOFTWARE DEVELOPED IN UNAM FACILITATES:
1. The organization, storage and processing of millions of climate data
(monthly temperature and precipitation).
2. The calculation more accurate of potential evapotranspiration.
3. The calculation of agroclimatic indices: humidity, aridity, erosion by
rainwater, among others; improving agricultural activities and reducing
damage to the environment.
4. The calculation of the continuous rainy season, which is vital to choose crop
varieties, optimizing the rainwater uses (helping the conservation of
aquifers) and achieves a greatest economic yield.
5. Identifying the trends of climate change at the local level (meaning and
magnitude), which allows the prevention of adverse effects and harnessing
the positive effects of this climate change.
.