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1. a o o o ae gt 9 a o o ae o 45 46 47 ABSTRACT During the past four years 1988 1991 the United States Department of Agriculture USDA performed an experiment testing a theory known as the Thermal Kinetic Window TKW theory This theory proposes that each species of crop can have an optimal yield if its canopy temperature can be kept within a window of temperatures The main crop of study was cotton which has a TKW between 23 C and 32 C An extensive amount of data was collected over the four years of study The main purpose of this paper will be to present a method of extracting certain pieces of this data so that meaningful analyses can be performed to determine the permissiveness of the environment in allowing the canopy temperature to remain within the TKW Some of these analyses will also be included in this paper vii CHAPTER I INTRODUCTION THE EXPERIMENT The growth and maturity of cotton varies greatly throughout the season due to the many environmental characteristics acting upon the crop Elements such as wind radiation humidity and air temperature can in excessive quantities affect the growth and maturity of each plant Due to the fact that these en vironmental elements are not controllable theories have been developed which suggest that certain plant characteristics may be altered in order to aid the plant to adjust to the environmental factors Two such charact2. oor or 0 99774 0 92779 0 99790 0 94629 0 99888 0 93209 0 99586 noon I oor too oar too 0 95510 0 99220 0 94218 0 98378 0 0001 0 0001 0 0001 0 0001 0 99870 0 94171 0 99598 0 95608 0 99880 noon amom oor bano oo oao 0 96578 0 99093 0 94996 0 98907 0 95683 0 98903 0 0001 0 0001 0 0001 0 0001 D W2 23 Table 3 1 cont WE pv ww wn r2 w bul Ero 0 99591 0 95315 0 99774 0 95510 0 99870 0 96578 0 92193 0 98935 0 92779 0 99220 0 94171 0 99093 I I 0 99579 0 94270 0 99790 0 94218 0 99598 0 94996 W30 0 98415 0 93830 0 97229 0 94629 0 98378 0 95608 0 98907 0 93924 0 99603 0 94509 0 99888 0 94562 0 99880 0 95683 0 98719 0 92621 0 98631 0 93209 0 99644 0 94466 0 98903 DF 0 93802 0 99724 0 94160 0 99586 0 94167 0 99234 0 94936 WF 1 00000 0 93590 0 97409 0 93656 0 98471 0 94673 0 98314 0 0 0 0001 0 0001 DV 0 93590 1 00000 0 93663 0 99643 0 93677 0 99349 0 94832 Som 20 woo oor con coms x00 WV 0 97409 0 93663 1 00000 0 94271 0 99318 0 95380 0 98595 noon wor oar ooo ton tons 0 93656 0 99643 0 94271 1 00000 0 94350 0 99776 0 95496 d rie i bam os coon sor WD 0 98471 0 93677 0 99318 0 94350 1 00000 0 99146 toon
3. sv pp sp 0 99591 0 93128 0 99774 0 91108 0 18267 0 09836 0 18837 0 20519 E 0 99733 0 90544 0 99579 0 93504 0 9979 0 91033 boon soon aam ton noon vom baal Fed 0 42668 0 45615 0 44062 0 48044 0 47355 lad 0 89797 0 99603 0 92999 0 99888 0 90858 0 95106 0 94015 0 94893 0 93182 DF 1 0 92405 0 99724 0 95064 0 99586 0 91628 ERE 0 0001 0 0001 0 0001 SF 0 92405 1 0 91721 0 96715 0 90016 0 91032 NE INN 0 0001 0 0001 0 0001 DV 0 99724 0 91721 1 0 95161 0 99643 0 91563 Dame aso som ean vao SV 0 95064 0 96715 0 95161 1 0 93339 0 91932 com sor omoi tom coon 0 99586 0 90016 0 99643 0 91172 0 91628 0 91032 0 91563 0 91932 0 91172 1 ub 0 0001 0 0001 0 0001 0 28 29 Table 3 4 Data for time series analysis The range of days was chosen from 171 297 due to the fact that an interval was needed that was contained within each year The times where chosen such that one measurement was from the coldest part of the day 700 one from the midrange 1200 and one from the hottest 1600 Choosing the times in this manner allows the study of the temperature variations throughout the day 3 3 1 Analyzing the Morning Data The first step in the analysis is to plot the data in order to determine if any trends are apparent such as cyclic upward or downward trends E
4. autocorrelation PACF plots were analyzed By observing each of these plots a preliminary model can be determined in order to begin the analysis On each plot there is one line on each side of the horizontal axis These lines are the 9596 bounds for the autocorrelations of a white noise sequence They are computed by the following formula 1 96 n If the data is a sample from an independent identically distributed sequence then approximately 95 of the autocorrelations should be within these bounds Observing the ACF plot reveals the possible moving average portion of the model by counting the number of lines between the beginning value and the last line that extends above the limits The PACF plot reveals the possible auto regressive portion of the model in the same manner Thus the model suggested by the ACF and PACF for the morning data from 1988 is an ARMA 1 11 Figure 3 5 35 Figure 3 6 ACF and PACF for 1989 The next step is to estimate the parameters of this model An option in PEST allows one to perform this estimation by entering the ARMA p q model suggested by the plots Upon entering the ARMA 1 11 model the program returns with a message stating that the model chosen is not causal which implies that the autoregressive portion of the model has a zero within the unit circle Therefore since there is only one auto regressive coefficient the next logical model to try is an ARMA 0 11 or MA 11 model The program wil
5. tem oon coon or oor soon 0 94673 0 99349 0 95380 0 99776 0 95452 1 00000 0 96639 W2 0 98314 0 94832 0 98595 0 95496 0 99146 0 96639 1 00000 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0 W32 24 Naturally all the entries along the main diagonal are 0 0 due to the fact that each treatment is being compared to itself Thus the null hypothesis is rejected Similar results were found for the data from 1989 in Table 3 2 With these results it is reasonable to assume that the same conclusions can be obtained regardless of whether drybulb or wetbulb data was used in the analysis Thus the remaining analyses will be performed using only the drybulb data from each treatment 3 2 Air versus Canopy Another correlation analysis was performed between the air temperature and the canopy temperature If there is a strong correlation between these two mea surements the difference between the the measurements should remain close to zero Table 3 3 shows the results of this analysis This analysis is based on the same weekly averages as the previous correla tion analysis between drybulb and wetbulb One can see by comparing the air temperature averages with their respective IRT averages that they are highyly correlated with the exception of the 28 C and the 30 C treatments The 28 C treatment claims that p 23096 with a p value 289 This implies that the null hypothesis Ho p
6. 4 0 HT dry furrow 2 5 HT 28 C 2 meters air only Enter the desired code 1 Figure 2 11 cont TIME SUBMENU CODE FUNCTION Analyze intermittent time intervals Analyze entire day Enter the desired code Figure 2 12 Time submenu from program USDA 2 2 6 Retrieving the data After all of the specifications have been made as to exactly which pieces of the data are needed for the analyses the user should select option 6 At this time the program will take over and extract exactly those pieces of data chosen 19 TIME SUBMENU CODE FUNCTION Analyze intermittent time intervals Analyze entire day Enter the desired code 1 Enter the number of time intervals for analysis 1 96 3 Enter the beginning time for interval 1 0 2345 15 min increments 700 Enter the ending time for interval 1 0 2345 15 min increments 700 Enter the beginning time for interval 1 0 2345 15 min increments 1200 Enter the ending time for interval 1 0 2345 15 min increments 1200 Enter the beginning time for interval 1 0 2345 15 min increments 1600 Enter the ending time for interval 1 0 2345 15 min increments 1700 Figure 2 13 Entering the times for the example The data will be placed into separate files depending on the type and the year of the data As each file for a chosen day is read a message will appear on the screen stating that the program is currently working on that day This will give the user some i
7. as the p value gets smaller the null hypothesis is more likely to be rejected Notice that with the exception of the cells along the main diagonal each of the lower values are 0001 which also implies that the two methods of measuring the temperature are significantly correlated 21 22 Table 3 1 Correlation analysis between drybulb and wetbulb for 1988 we DF M uw 0 94159 0 99731 0 95766 0 99880 0 94683 0 99608 00 coon oam aon coon wor oor 1 00000 0 92459 0 97449 0 93140 0 98921 0 92511 Boi es orn tor oo wooo dE 1 00000 0 94380 0 99867 0 93152 0 99733 Ga 00 coon omm con ooo W30 Fra 0 97449 0 94380 1 00000 0 94812 0 98575 0 93984 coma oar noon oom H ano 0 99867 0 94812 1 00000 0 93522 0 99545 comm sam W32 0 94683 0 98921 0 93152 0 98575 0 93522 1 00000 0 93150 Elli ae nd F 0 99608 0 92511 0 99733 0 93984 0 99545 0 93150 1 00000 peed Pend Ein F 0 95146 0 97930 0 93543 0 98415 0 93924 0 98719 0 93802 Sao ozo oso som oom oom oro 0 99591 0 92193 0 99579 0 93830 0 99603 0 92621 0 99724 San oso oso oso os oom oor Jg 5995292 5 V V 0 95315 0 98935 0 94270 0 97229 0 94509 0 98631 0 94160 uon wow mor eom
8. days within that year Enter the day i beg end where i is the z day to be entered and beg and end are the first and last days of the year respectively Finally option 4 allows the user to select all of the days of the year without having to enter each day separately If this option is chosen the program will automatically enter the days for each year selected After the days have been chosen the main menu will appear on the screen Figure 2 1 Since the example extracts the data over all four years the menu in Figure 2 5 will appear four times on the screen Figure 2 6 Figure 2 7 Figure 2 8 and Figure 2 9 2 2 4 Entering the treatments In order to select the treatments for analysis the user will select option 4 from the main menu Figure 2 1 Since for some years drybulb and wetbulb data had been collected the program will first prompt the user to select which type of data is to be extracted Figure 2 10 12 DAY MENU CODE FUNCTION Analyze one day Analyze succesive days Analyze intermittent days Analyze entire year Enter the desired code Figure 2 5 Day menu for program USDA DAY MENU CODE FUNCTION Analyze one day Analyze succesive days Analyze intermittent days Analyze entire year Enter the desired code 2 Enter the number of intervals for analysis 1 160 1 Enter the beginning day of interval 1 161 318 195 Enter the last day of interval 1 161 318 250 Figure 2 6 Enter
9. results was 37 Figure 3 8 ACF and PACF for 1991 X t Z t 280Z t 1 263Z t 2 244Z t 4 265Z t 5 275Z t 6 The final results are found in Table 3 6 Thus the results for this model reflect the same conclusion as the other years 3 3 2 The Noon Data The plots of the data collected at noon throughout the years reveal al most the same characteristics as the plots from the morning values Figure 3 9 Figure 3 12 However the spread of the data is larger than the spread found in the morning More than likely this is caused by the fact that the temperature of the plant does not increase quite as rapidly as the temperature of the air 38 Table 3 5 Results of Model ARMA 0 11 Data used 9 6 2 3 1 92668 0 5734 1 59615 0 5039 1 31676 0 8833 0 94214 0 1579 0 49526 1 1048 L Obs Com 0 0 49279 Q 0 4 0 4 9 2 4 D 4 Computed Obs Com 1 2 Observed Data y 0 99661 0 8034 0 17222 1 0278 Table 3 6 Results of Model ARMA 0 6 Data used 0 0 1 2 0 7 1 4 os 64x05 1321 39 0 42855 2 47145 0 45331 1 2533 0 6 1 0 C 0 3 0 0 Observed oa eres osa 09 0 42855 0 4715 L3 0 45331 1 7533 Data ed 0 7 0 2 0 9 3 8 9 0 4 4 Observed Computed 45 0 08000 4399 as omo 24n Taan aes 38 1
10. 0 0 91905 0 99387 Pale 0 90387 1 00000 0 91787 0 98698 0 94217 0 99113 0 92299 me uam coon oso cows oon 0 99420 0 91787 1 00000 0 90625 0 98319 0 93510 0 99926 l a on oa oan oo 0 90630 0 98698 0 90625 1 00000 0 95259 0 97290 0 91068 WD 0 98750 0 94217 0 98319 0 95259 1 00000 0 94619 0 98310 a PE 0 0001 0 0 0 0001 0 0001 0 91905 0 99113 0 93510 0 97290 ld e 0 0001 0 0000 0 0 0 0001 W2 0 99387 0 92299 0 99926 0 91068 0 98310 0 94117 e 0 0001 0 0001 0 0001 0 0 Table 3 3 Correlation analysis between Air and IRT Temperatures D28 sz D30 sso ps2 s32 ae es 0 99731 0 47428 0 9988 0 95503 0 1693 0 05589 0 20669 0 37419 1 0 48763 0 99867 0 94332 1 0 49181 0 53492 0 0222 08 0 0183 0 99867 0 49181 1 0 95063 0 95503 0 37419 0 94332 0 53492 0 95063 1 0 99608 0 16188 0 99733 0 4582 0 99545 0 94579 0 90184 0 09467 0 90544 0 42668 0 89797 0 91107 0 99591 0 18267 0 99579 0 45615 0 99603 0 95106 0 93128 0 09836 0 93504 0 44062 0 92999 0 94015 0 99774 0 18837 0 9979 0 48044 0 0203 0 0001 0 0001 0 91108 0 20519 0 91033 0 47355 0 90858 0 93182 0 0001 0 3476 0 0001 0 0225 0 0001 0 0001 DF SF SV ai 27 Table 3 3 cont oF s
11. 0 will be rejected only if a significance level of 28 996 or greater is chosen which is unrealistic Therefore Ho will not be rejected Com paring the D30 and S30 variables the analyst finds that Ho will be rejected as long as a significance level over 1 896 is used for the test The remainder of the variables ensure that Ho will be rejected for almost any significance level desired 3 3 Analyzing the Data as a Time Series Since the study performed by the USDA concluded that the 28 C treatment has the highest yield in relation to the amount of water used the remainder of this chapter will concentrate on this treatment only The next type of analysis that was performed was a time series analysis to see if a model can be determined by the data so that anyone will be able to predict future results In each of the following subsections a different aspect of the analysis will be addressed The data used in each of the analyses is described in Table 3 4 25 Table 3 2 Correlation analysis between drybulb and wetbulb for 1989 pss wzs pze wa poe wooo DF Md S d 0 99740 0 93153 0 99764 0 92807 0 99811 Mur dg 0 89992 0 99151 0 89902 0 99685 0 91888 0 89992 1 00000 0 92665 0 99639 0 92103 0 99570 adl 0 99151 0 92665 1 00000 0 91958 0 99707 0 93666 0 99639 0 91958 1 00000 0 91732 0 99504 W262 0 92807 0 99685 0 92103 0 99707 0 91732 1 00000 0 93350 i Fd
12. 28 C Finally in 1991 only the 28 C treatment was studied as 8 temperature controlled plot Over the four years an immense amount of data was collected considering that the temperature readings were recorded every 15 minutes of every day for an average of 150 days each year So that proper analyses could be performed on this data a system was developed that would allow the analyst to extract certain pieces of the data depending on what types of tests were to be analyzed The main purpose of this study was to develop such a system through the use of FORTRAN programs In the following chapters an explanation of the programs and some analyses performed through the use of these programs will be given In chapter 2 a user s manual for the main program that actually extracts the data for analysis is provided with an example while in chapter 3 there will be a discussion of some of the analyses performed as well as a discussion of other programs used in each analysis Finally in chapter 4 results of the analyses and possible future analyses will be discussed CHAPTER II USER S MANUAL 2 1 Getting Started Before the program can be run the user must make sure that the data is properly set up and in the right directories For some years a drybulb and wetbulb temperature was recorded However even though the wetbulb data may not have been collected for a certain year the data must appear as if it had been During times when some piece of equip
13. ONS In experiments such as the one performed by the USDA it is common to ob tain tremendous amounts of data Due to the vastness of the data sets any type of analysis becomes difficult and cumbersome However with the development of the USDA program the data can be broken up into smaller pieces depend ing upon what type of analysis is to be performed The program which allows the user to extract any piece of data from the large set provides a user friendly atmosphere so that any person can use the program without difficulty At the current time the program is set up to analyze only the data collected from 1988 to 1991 However an upcoming revision will contain an option that will allow the user to input any year for which data has been collected He will have to input the year range of days and treatments for each additional year Once this option has been added the program will be more versatile with the exception of the manner in which the data must be set up The data will have to maintain the format specified in Section 2 1 The analyst will thus be able to use this program to perform any type of analysis on any data collected in the future as well as that which has already been obtained As a result of the time series analysis performed in this study the analyst should consider the possibility that this data cannot be modelled using this type of analsis However one should try to determine if there exists any deterministic trend or ra
14. STATISTICAL ANALYSIS ON ENVIRONMENTAL LIMITATIONS ON THRESHOLD BASED IRRIGATION MANAGEMENT by MARK TODD LUEDECKE B S A THESIS IN STATISTICS Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Approved Accepted May 1992 ETSI ZOE 1 992 No 16 ACKNOWLEDGMENTS Cep Z I would like to thank my committee members Dr Truman Lewis Dr Benjamin Duran and Dr Hossein Mansouri not only for their assistance on this project but also for the education which they provided me I would also like to thank the United States Department of Agriculture specif ically Don Wanjura Dan Upchurch and James Mahan for providing the data for this study Most of all I would like to thank my parents for the financial support and the encouragement that they gave me throughout my college years H CONTENTS ACKNOWLEDGMENTS 9 9 RR RS ii LIST OF TABLES 5 5 ni ee eck R Te ye Ute e hana fn ie mee iv LIST OF FIGURES 5 3i ose t wd as SS Oe ee v ABSTRACT sosiaa eS aopen d vii I INTRODUCTION THE EXPERIMENT 1 IL USER S MANUAL eed EAE SS Wd Se RENE 5 2 1 Getting Started uo x RE SR ban E EE 5 2 2 Running the Program 6 2 21 Entering the 6 2 22 Entering the types ce 8 2 2 3 Entering the days 9 2 2 4 Entering th
15. ach of the following analyses will use the difference between the air temperature and infra red thermometer temperature The first four figures show the plots of the morning differences for each year Figure 3 1 Figure 3 2 Figure 3 3 and Figure 3 4 Notice in each figure that the values are for the most part close to a value of zero By studying these plots one can see that there is not any apparent upward or downward trend This is marked by the fact that as the days increase the temperature differences do not continually decrease or increase The plots do not show any obvious signs of repetition which implies the absence of a cyclic trend Therefore at first glance one would expect that the data is stationary with no deterministic trends The next step is to try to model the data This process was attempted with the aid of a program called PEST by Peter J Brockwell and Richard A Davis In order to do any analyzing with PEST amp model must first be entered Thus after entering the morning data for 1988 the autocorrelation ACF and partial Temperature Day of Year Figure 3 1 Plot of morning values for 1988 30 Temperature Day of Year Figure 3 2 Plot of morning values for 1989 31 Temperature Day of Year Figure 3 3 Plot of morning values for 1990 32 Temperature Day of Year Figure 3 4 Plot of morning values for 1991 33 34 Figure 3 5 ACF and PACF for 1988
16. adiation being reflected by the plant Through the use of a computer system and the IRT s the were measured every 15 seconds Then an average of these readings was calculated every 15 minutes and recorded These averages were performed twenty four hours a day seven days a week throughout the growing season Therefore based on the 15 minute average readings from the IRT s the USDA developed the irrigation schedules that would decrease water stress and hopefully improve overall yield In order to perform a useful analysis the USDA set up several plots of cotton each receiving a different irrigation schedule One plot of land was irrigated each week based on the standard method of observing the soil water profile If the profile of the water in the soil was substantially decreased water was applied in order to replenish the water level This treatment will be referred to as the Soil Water Replacement Fixed SWRF treatment and will be used as the con trol plot Another plot of land was designed to implement a watering schedule at variable times depending on when the soil water profile was substantially de creased however this method was more lenient than the SWRF treatment Most times this plot of land was irrigated every two weeks This treatment is called the Soil Water Replacement Variable SWRV treatment Another plot was de signed to receive only the initial preplant irrigation and the rainfall thereafter This treatment will be r
17. ch as SAS and PEST could be used for the analyses 3 1 Drybulb versus Wetbulb One such program computed the averages of the air temperatures from 1988 and 1989 over a one hour time period between 12 00 pm and 1 00 pm These averages were then used to compute weekly averages and a correlation analysis was performed on these averages using SAS to test if there was a significant difference between the drybulb and wetbulb data to justify using both types of information in each analysis Table 3 1 shows the results of that study for 1988 In each cell of Table 3 1 two pieces of information are given The numbers on the top in each cell are the Pearson Correlation Coefficients which describe how closely each treatment is linearly related to each of the others The correlation coefficient will always be a number between 1 0 and 1 0 If the coefficient is close to either of the endpoints the treatments are said to be highly correlated If the number is close to 0 0 the treatments are not linearly correlated In each instance the correlation coefficient is a value very close to a value of 1 0 which suggests that the two methods of measuring the temperature are strongly correlated The null hypothesis that is being tested with this procedure is Ho p 0 where p is the correlation coefficient against H4 p 0 The bottom number in each cell called the p value is the smallest significance level at which the null hypothesis can be rejected In general
18. dea of the length of time that will be required for each file Once the program has completed the extraction the main menu will appear on the screen and the user may begin over and select other data for different analyses However if the user wishes to save the files created by the program he must exit the program and rename the files that were created If the user fails to rename the files they will be deleted and rewritten with the new data 2 2 7 Stopping the program If at any time the user decides not to extract the data or he finishes extracting data he can select option 7 from the main menu If this option is chosen any options that were inputted without being extracted will be lost For example if 20 the operator enters the years types and days and then selects option 7 from the main menu the DOS prompt will appear and the years types and days that he entered will be lost The data files will not be deleted but the options will have to be re entered All files formed by this program will not be deleted unless the user chooses to do so at the DOS prompt or if the program is run twice CHAPTER III ANALYZING THE DATA The USDA program has proven to be a major tool in the analysis of the data provided by the Department of Agriculture However this program is strictly used to extract data and does not have any analyzing capabilities Other pro grams were implemented in order to put the data into 8 form so that software su
19. e 11 2 2 5 Entering the times 15 2 2 6 Retrieving the data 18 2 2 7 Stopping the program 19 ANALYZING THE DATA 21 3 1 Drybulb versus Wetbulb een 21 3 2 Air versus Canopy 9 Rs 24 3 3 Analyzing the Data as a Time Series 24 3 3 1 Analyzing the Morning Data 29 3 3 2 The Noon Data SS SORES OSS 37 3 833 The Evening Data 40 3 3 4 An Interesting Result aeae 48 IV CONCLUSIONS lt eg agg ERU e E OE ARE a 50 51 iii 1 1 2 1 3 1 3 2 3 3 3 4 3 5 3 6 3 7 LIST OF TABLES Six treatments with water use and lint yield for 1988 Example of an application of program USDA Correlation analysis between drybulb and wetbulb for 1988 Correlation analysis between drybulb and wetbulb for 1989 Correlation analysis between Air and IRT Temperatures Data for time series analysis Results of Model ARMA 0 11 Results of Model ARMA 0 6 Results of Model ARMA 181 iv 22 25 27 29 38 39 49 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 LIST OF FIGURES Main menu from program USDA
20. e number of types for analysis 1 6 This prompt allows the user to extract anywhere from one to six types of data at a time After entering the number of types to extract the output that will appear on the screen can be found in Figure 2 3 This screen will be shown as many times as the number of types chosen above If for some reason the user enters the same type more than once the program will give an error message stating that the type has already been selected and will ask the user to type a carriage return The output appears in Figure 2 4 Again the program will now return to the main menu Figure 2 1 TYPE MENU CODE TYPE Air temperature Infra red thermometer Radiation Wind Yield Irrigation control Enter the desired code Figure 2 3 Type menu from program USDA 2 2 3 Entering the days The next option to be chosen should be option 3 which allows the user to specify which days he wants to extract Upon selecting this option a new menu will appear on the screen giving the user a variety of ways to select the days for analysis Figure 2 5 p 12 Again this menu will appear on the screen as many times as the number of years chosen This option has been added in case the user wants to select different days from each year The operator can opt to analyze only one day of the year by selecting option 1 or he can select a number of days by selecting one of the options 2 4 depending on which suits his needs If o
21. eee Year menu from program Type menu from program USDA Entering the types for example Day menu for program USDA Entering the 1088 Entering the days for 1989 eee Entering the days for 1990 Entering the days for 1991 Treatment menu from program USDA Treatment submenus from program USDA with examples Time submenu from program USDA Entering the times for the example Plot of morning values for 1988 Plot of morning values for 1989 ln Plot of morning values for 1990 Plot of morning values for 1991 ACF and PACF for 1988 x ea ACF and PACF for 1989 263s a 9x ee LEUR IS ACF and PACF for 1990 ACF and PACF for 1991 ah eo oe 4 Plot of noon values for 1988 Plot of noon values for 1989 Plot of noon values for 1990 Plot of noon values for 1991 ln 10 12 12 13 13 14 14 16 18 19 30 31 32 33 34 35 36 37 40 41 42 43 3 13 Plot of evening values for 1988 3 14 Plot of evening values for 1989 3 15 Plot of evening values for 1990 3 16 Plot of evening values for 1991 e 9
22. eferred to as the dryland DRY treatment Throughout the study at most three plots of land were designed to monitor the periods of irrigation based on the T of the plant The base temperature varied by 2 C between each plot of land If after any 15 minute period the T exceeded the threshold temperature set for that plot the irrigation process would begin and remain on throughout the next 15 minute period If after the end of that period the was still above the threshold irrigation would continue In 1988 the three temperature treatments that were studied were 28 C 30 C and 32 C as well as the SWRF SWRV and DRY treatments The following Table 1 1 gives the final results of each of the six different treatments in terms of the total water applications and the overall lint yield Table 1 1 Six treatments with water use and lint yield for 1988 250 applied Lint Vila 29 C oem une 20 C asem 1079 22 C 35cm 108 SWRF 198 cm 1490 M SWav em nar DRY om 3892 After observing the overall yield in comparison to the amount of water applied to each plot the USDA came to the conclusion that the 28 C treatment had a sufficiently greater lint yield 1 Over the next three years they concentrated on temperatures close to 28 C In 1989 they used 26 C 28 C and 30 C as the temperature treatments In 1990 they studied only two plots with different base temperatures 26 C and
23. eristics which have been a focus of the USDA are water stress and canopy temperature Water stress is amp condition in the plant which causes a deficiency of the requirements needed for proper transpiration in the plant As the plant is exposed to both the soil and the atmospheric conditions the soil moisture level determines the soils ability to supply water to the plant depending on the atmospheric conditions at the time For example in areas where the relative humidity is high the plant temperature will tend to remain constant with the air temperature and in semi arid areas such as the Lubbock locale where the humidity level is usually around 20 3096 the temperature of the air will usually be 2 4 higher than the temperature of the plant One method that is generally used to determine whether or not the plant is suffering from water stress is to inspect the foliage to see if any wilting is present Another more scientific method is to observe the canopy temperature and the air temperature This method is useful in determining the level of water stress through the derivation of the crop water stress index CWSI developed by Idso et al 1981 3 The CWSI provides an upper and lower limit for at any deficit of vapor pressure Water stress has proven to be a major criterion in the development of the cotton during the flowering and boll development stages 1 Through the ob servation of the canopy temperatu
24. ing the days for 1988 13 DAY MENU CODE FUNCTION Analyze one day Analyze succesive days Analyze intermittent days Analyze entire year Enter the desired code 2 Enter the number of intervals for analysis 1 144 1 Enter the beginning day of interval 1 171 304 195 Enter the last day of interval 1 161 318 250 Figure 2 7 Entering the days for 1989 DAY MENU CODE FUNCTION Analyze one day Analyze succesive days Analyze intermittent days Analyze entire year Enter the desired code 2 Enter the number of intervals for analysis 1 139 1 Enter the beginning day of interval 1 158 297 195 Enter the last day of interval 1 161 318 250 Figure 2 8 Entering the days for 1990 14 DAY MENU CODE FUNCTION Analyze one day Analyze succesive days Analyze intermittent days Analyze entire year Enter the desired code 2 Enter the number of intervals for analysis 1 152 1 Enter the beginning day of interval 1 155 307 195 Enter the last day of interval 1 161 318 250 Figure 2 9 Entering the days for 1991 Analyze drybulb Analyze wetbulb Analyze both Enter the desired code Figure 2 10 Treatment menu from program USDA 15 After the type of temperature readings have been selected the program will prompt the user to enter the number of treatments for the year currently being considered Enter the number of treatments for year 1 tot The treatment submenu for that yea
25. l list the coefficients of each of the terms followed by the ratio of each estimate to its standard error Se times 1 96 The values S 1 96 which are less than 1 0 suggest that those coefficients could possibly be zero After preliminary estimation of the parameters PEST will optimize those estimates using one of two methods maximum likelihood or least squares The optimum model chosen by PEST for the ARMA 0 11 model is as follows 36 Figure 3 7 ACF and PACF for 1990 X t Z t 533Z t 1 415Z t 2 525Z t 3 544Z t 4 454Z t 5 171Z t 10 Choosing several pieces of the data to test the model the following results were obtained when trying to predict future values Table 3 5 Observing the error terms in the last column of each table one can see that the model is not predicting the actual observed values very well Thus a natural assumption is that some type of trend exists which is not evident This idea is justified by Brockwell and Davis 4 They claim that if on the ACF plot the values decrease slowly then some trend may be involved with the data The same results are obtained for 1990 and 1991 Figure 3 7 and Figure 3 8 Due to the fact that the ACF and PACF plots for 1989 morning data do not resemble any of the plots for the other years the different model chosen was an ARMA 0 6 Figure 3 6 The same procedures were run for this data and the model determined by these
26. mbination of years Figure 2 2 Table 2 1 Example of an application of program USDA 1988 1989 1990 1991 AIRRT 195 250 drybulb 28 C 700 1200 1600 1700 MAIN MENU CODE FUNCTION Enter the years for analysis Enter the types for analysis Enter the days for analysis Enter the treatments for analysis Enter the times for analysis Get the data Quit Enter the desired code Figure 2 1 Main menu from program USDA If the user chooses to analyze the data within one year Option 1 he will then be prompted to enter which year is to be analyzed Enter the year for analysis However if the operator chooses option 2 the program will prompt him to enter the number of years for analysis and the years Thus following the example the user will select option 2 and answer the prompts accordingly YEAR MENU CODE FUNCTION Perform analysis within 8 year Perform analysis among years Enter the desired code Figure 2 2 Year menu from program USDA Enter the number of years for analysis 4 Enter the year 1 for analysis 1988 Enter the year 2 for analysis 1989 Enter the year 3 for analysis 1990 Enter the year 4 for analysis 1991 At this time the program will return to the main menu Figure 2 1 2 2 2 Entering the types The user should enter the types of data to be analyzed by selecting option 2 Upon selecting this option the operator will receive the following prompt Enter th
27. ment may not have been operating properly a missing value number was recorded in place of the bad data This number is represented by 99 0 in this study Therefore if during some year the proper amount of data had not been collected a column of missing values should be placed into the data set in the respective position Each data file must be sixteen columns wide with the first column containing the day of the year The second column represents the time of the day beginning with 0 and going through 2345 in 15 minute intervals The other fourteen columns will contain the data with every odd column being the drybulb data and every even column the wetbulb data After each file has been properly formatted the user must put the files into their respective directories The data files should be placed in the subdirectory corresponding to its year and data type USDA year type For example the air temperature data from 1988 should be placed into the USDA 1988 AIR subdirectory Each file must also be properly named in order for the program to be able to locate it Each file which contains the data for a certain day must have the following format typeday DAT For example AIR163 DAT is the air temperature for day 163 In each instance above type will be one of the following AIR IRT RAD WIN or CONT AIR is the air temperature data IRT is the infra red ther mometer data RAD is the radiation data WIN is the
28. ndom trend that is affecting this data In addition they should consider for other possible methods that would describe the characteristics of this data The number of analyses that can be performed using the current data is endless The analyses performed in this study dealt strictly with a very small portion of the air temperatures and canopy temperatures even though many other environmental elements exist that will affect the growth of the plants In addition the other environmental elements should be analyzed to see what substantial effect they might have on the growth and maturity of the cotton plant 90 REFERENCES 1 D F Wanjura D R Upchurch J R Mahan Evaluating Decision Criteria For Irrigation Scheduling of Cotton Transactions of the ASAE Vol 33 No 2 pp 512 518 1990 2 J R Mahan J J Burke K A Orzech The Thermal Kinetic Window as an Indicator of Optimum Plant Temperature Plant Phisiology Supply 83 87 1987 3 D F Wanjura J L Hatfield D R Upchurch Crop Water Stress Index Relationships with Crop Productivity Irrigation Science 11 pp 93 99 1990 4 P J Brockwell and R A Davis ITSM An Interactive Time Series Modelling Package for the PC Springer Verlag pp 16 17 1991 91
29. ption 1 is chosen the following prompt will appear on the screen Enter the day for analysis beg end where beg is the first day of the year and end is the last day of the year If the user wishes to extract one or more intervals of days the best option to choose is option 2 which yields these prompts Enter the number of intervals 1 num where num is the number of days in that year for which data was collected 10 Enter the number of types for analysis 1 6 2 Enter the desired code 1 Air temperature Infra red thermometer Radiation Wind Yield Irrigation control TYPE MENU CODE TYPE Enter the desired code 2 Air temperature Infra red thermometer Radiation Wind Yield Irrigation control Figure 2 4 Entering the types for example 11 Enter the beginning day of interval i for analysis beg end where i is the 1 interval to be entered Enter the last day of interval i for analysis beg end If for some reason the days entered are not within the specified interval or if the beginning and last days are not in the right order an error message will be given and the user will be prompted to start over If the user wants to select one day here and there he should select option 3 In this instance the program will first prompt for the number of days to be selected and then will prompt for the specific days Enter the number of days for analysis 1 num where num is the number of
30. r will then appear on the screen the same number of times as selected above Each of the possible submenus will be demon strated through the use of the example Figure 2 11 After the treatments have been entered the program will return to the main menu Figure 2 1 2 2 5 Entering the times The final criterion that the user needs to specify is the times of the day that he wants extracted This is accomplished by selecting option 5 from the main menu Figure 2 1 The operator will then have the option to either enter the times in intermittent intervals or enter the entire day Figure 2 12 If option 1 is chosen the program will prompt for the number of intervals that will be included in the analysis Enter the number of intervals for analysis The next two prompts will ask for the beginning and ending time for the 1 interval These prompts will be repeated as many times as the time intervals chosen If the beginning and ending times for any particular interval are not in the right order a run time error will occur the program will end and the DOS prompt will appear Notice that 1 00 pm is denoted as 1300 not as 100 It is very important that these numbers are input properly Enter the beginning time for interval i 0 2345 15 min increments Enter the ending time for interval i 0 2345 15 min increments The program will enter all of the times in between the beginning and ending times provided If option 2 is chosen
31. re an irrigation schedule was developed that would adjust the water stress level of the plant In addition this irrigation sched ule allowed the USDA to test the TKW theory developed by J R Mahan et al 1987 2 This theory suggests that if the canopy temperature of the plant was maintained within the window set for its species specifically 23 C and 32 C for cotton then the overall yield would be increased with more efficient water usage The USDA also theorized that within the TKW there exists an interval of normalized temperatures which the plant tries to maintain when spe cific environmental conditions are satisfied The T for cotton is between 26 C and 30 C and these temperatures became the main focus of the USDA study They found that the optimal yield in relation to fiber length and strength was obtained when the was kept within these values The USDA was able to observe the through the use of infra red thermome ters IRT s Two IRT s were placed on each of the plots of land one on the north side and one on the south side On each plot of land there were eighteen 30 5 meter rows of cotton that were spaced 76 cm apart and ran from east to west One of the advantages to using the IRT s as opposed to other temperature read ing devices is that the IRT s do not touch the plant at any point which allows the plant to remain in a natural state The IRT s read the temperature by in putting the amount of heat and r
32. rire np an see DF 0 99811 0 91888 0 99570 0 93666 0 99504 0 93350 1 00000 WF 0 91809 0 99668 0 90972 0 99589 0 90692 0 99813 0 92434 a es aoe DV 0 98608 0 90074 0 98346 0 91457 0 98442 0 91213 0 98953 now sar oom tam orn vom WV 0 91782 0 99558 0 90754 0 99091 0 90656 0 99274 0 92640 wore aso tom ten tor soo WD 0 95924 0 98392 0 95168 0 98872 0 95255 0 97605 0 92095 0 96684 0 92354 0 0001 0 0001 0 0001 0 0001 0 0001 0 92243 0 99446 0 91226 0 99044 0 91083 0 99201 0 93172 0 99776 0 89930 0 99722 0 91973 0 99771 0 91726 0 99642 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 0 0001 26 Table 3 2 cont we w pp w w e en L 0 99776 0 95924 0 97605 0 92243 0 0001 0 0001 0 0001 SEN 0 89930 0 98392 0 92095 0 99446 0 0001 0 0001 0 0001 0 90754 0 99722 0 95168 0 96684 0 91226 0 91457 0 99091 0 91973 0 98872 0 92354 0 99044 e 0 98442 0 90656 0 99771 0 95255 0 96942 0 91083 0 99813 0 91213 0 99274 0 91726 0 99019 0 92457 0 99201 Ferd bed peed rd eed Ped DF 0 92434 0 98953 0 92640 0 99642 0 96238 0 98316 0 93172 il Fen ead peel Pe dE WF 1 00000 0 90387 0 99420 0 90630 0 9875
33. rmed by taking the air temperature minus the canopy temperature T were used instead of analyzing A very interesting result occurred through this difference By multiplying the values used in the previous analyses by 1 0 the models suggested by the ACF and PACF plots changed drastically In most cases the model chosen was an ARMA 18 1 model In addition the predictions formed by this model were significantly close to the observed values This is another curiosity that should be studied further X t Z t 4 922X t 1 075X t 2 108X t 3 158X t 4 035 X 1 5 4 213X t 6 141X t 7 095X t 8 297X t 9 312X t 10 016 X t 11 220X t 12 059 X t 13 018X t 14 109 X t 15 086X t 16 084X t 17 033X t 18 305Z t 1 The results of this model can be found in Table 3 7 Notice that these results are closer to the real values than those from the previous models however other models should be tested for better accuracy 49 Table 3 7 Results of Model ARMA 18 1 Data used 2 5 3 2 0 6 1 2 0 7 1 4 1 1 1 2 0 9 9 0 8 0 6 Observed Computed Obs Com 06 01959 0 73983 pin 1 08985 1 78985 0 37916 0 87916 Data used 1 5 1 0 0 7 0 5 0 1 0 1 0 4 0 9 0 7 D 00909 00 3 1 08 10720 0279 0 97587 CHAPTER IV CONCLUSI
34. swm 2 4603 39 40 Temperature Day of Year Figure 3 9 Plot of noon values for 1988 The time series analysis of this data has very similar results to those of the analysis of the morning temperatures Therefore those analyses will not be included in this work 3 3 3 The Evening Data Again the plots of the evening data resemble those of the other two time periods Figure 3 13 Figure 3 16 They follow the noon values more closely than the morning values due to the fact that a larger increase in temperature usually occurs between 7 00 am and 12 00 pm than between 12 00 pm and 4 00pm Temperature Day of Year Figure 3 10 Plot of noon values for 1989 41 Temperature Day of Year Figure 3 11 Plot of noon values for 1990 42 Temperature Day of Year Figure 3 12 Plot of noon values for 1991 43 Temperature Day of Year Figure 3 13 Plot of evening values for 1988 Temperature Day of Year Figure 3 14 Plot of evening values for 1989 45 Temperature Day of Year Figure 3 15 Plot of evening values for 1990 46 Temperature Day of Year Figure 3 16 Plot of evening values for 1991 4T 48 The time series analyses for this time period closely resembles that of the morning and noon temperatures so again the analyses will not be provided in this paper 3 3 4 An Interesting Result question arose as to how the analyses would differ if the values fo
35. the program will automatically enter all times starting 16 TREATMENT MENU CODE FUNCTION Analyze drybulb Analyze wetbulb Analyze both Enter the desired code 1 Enter the number of treatments for 1988 1 7 1 TREATMENT SUBMENU FOR 1988 CODE FUNCTION 28 C 30 C 32 C Fixed soil water replacement Variable soil water replacement Drybase 2 meters air only Enter the desired code 1 Figure 2 11 Treatment submenus from program USDA with examples from 0 to 2345 without any prompting for the user Once completed the main menu will once again appear on the screen Since the example calls for only a few time points option 2 will be selected The user should notice that if only a single time is desired he will enter the same time for both the beginning and ending time Figure 2 13 Enter the number of treatments for 1989 1 8 1 TREATMENT SUBMENU FOR 1989 CODE FUNCTION Fixed soil water replacement 28 C treatment 1 28 C treatment 2 26 C CTV CTD 2 meters air only Enter the desired code 1 Enter the number of treatments for 1990 1 6 1 TREATMENT SUBMENU FOR 1990 CODE FUNCTION Variable soil water replacement 26 C 30 C 28 C Fixed soil water replacement 2 meters air only Enter the desired code 1 Figure 2 11 cont 17 18 Enter the number of treatments for 1991 1 6 1 TREATMENT SUBMENU FOR 1991 CODE FUNCTION 7 0 HT 5 5 HT 4 0 HT
36. wind data and CONT is the control data which specifies when the system was actually irrigating The year will be either 1988 1989 1990 or 1991 The day will correspond to the day that is recorded in that file The range of days varies from year to year The days range from 161 318 in 1988 171 304 in 1989 158 297 in 1990 and 155 307 in 1991 Once each of the above conditions has been met the program will work properly 2 2 Running the Program The program is not required to be in any certain directory however it must be on the same drive as the data preferably in the root directory In order to begin the program the following command must be entered CA USDA where USDA is the name of the program and the lt CR gt denotes a carriage return fter a few moments the main menu will appear on the screen Figure 2 1 By choosing each of the options available the user will be able to extract any portion of data that is desired Due to the fact that each year is different with respect to the days recorded and the treatments Option 1 should always be selected first Throughout the rest of this chapter the following example will be used in order to demonstrate the procedures of the program The data to be extracted is found in Table 2 1 2 2 1 Entering the years At times the user may not want to analyze all of the years so an option has been added which allows the operator to analyze either one year or any co
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