Thanks for the answer PaigeMiler. But, it isn't. I will share again the Appendix in the article. I only have the values of To, Tb and Tc, all the other must be estimated. Maybe I have to do a DO until code becasue I have to achieved the convergence, because in the end I only have one value of L and U (convergence), and this value I will sum in Tb (minimum temperature) and Tc (maximum temperature) to corret it. I read a lot this example in the article but it is very confuse to understand this iterative procedure. If we could continue to talk about this, I I appreciate it.   ... View more

Thanks for the anwser. Do you have any example to share about this DO until convergence.  I made this SAS program, but did not work again, because I can not see any changes in values. data temp; To=14; Tb=4; Tc=20; k=(Tc-To)/(To-Tb); l=(0.05**2)*(To-Tb)*((Tc-To)**k); do i=1 to 50 by 1; i+1= l/(((Tc-Tb)**(k+1))*((1-i)**k)); output; end; run; ... View more

I inform the values of To, Tb and Tc. data temp; To=14; Tb=4; Tc=20; k=(Tc-To)/(To-Tb); l=(0.05**2)*(To-Tb)*((Tc-To)**k); do i=1 to 50 by 1; i+1= l/(((Tc-Tb)**(k+1))*((1-i)**k)); output; end; run; However the log indicates an error: 416 data temp; 417 To=14; 418 Tb=4; 419 Tc=20; 420 k=(Tc-To)/(To-Tb); 421 l=(0.05**2)*(To-Tb)*((Tc-To)**k); 422 do i=1 to 50 by 1; 423 i+1= l/(((Tc-Tb)**(k+1))*((1-i)**k)); 424 output; 425 end; 426 run; NOTE: Division by zero detected at line 423 column 7. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. NOTE: Invalid argument(s) to the exponential operator "**" at line 423 column 32. To=14 Tb=4 Tc=20 k=0.6 l=0.0732539013 i=51 _ERROR_=1 _N_=1 NOTE: Missing values were generated as a result of performing an operation on missing values. Each place is given by: (Number of times) at (Line):(Column). 49 at 423:25 NOTE: Mathematical operations could not be performed at the following places. The results of the operations have been set to missing values. Each place is given by: (Number of times) at (Line):(Column). 1 at 423:7 49 at 423:32 NOTE: The data set WORK.TEMP has 50 observations and 6 variables. NOTE: DATA statement used (Total process time): real time 0.01 seconds cpu time 0.01 seconds Now, I don't know what is going on. In the article, the authors have said to start with L=0 and then proceed to the interaction until convergence is achieved. However, I still thinking that I'm not writting on right way.     ... View more

The "k" represents the range of temperatures where there are plant growth in the study. ... View more

Thanks for the answer.   The "k" and "l" are just index to converge L and U in the iterative process. Such as the steps in image below:               Because the model sometimes provide exagered Tb(base or minimum) and Tc(ceiling or maximum) temperatures, and this iteration process try to solve this problem by calculting L and U for recalculted Tb and Tc. In the process above To is optimum temperature. ... View more

Thanks for the answer.   The "k" and "l" are just index to converge L and U in the iterative process. Such as the steps in image below:             Because the model sometimes provide exagered Tb(base or minimum) and Tc(ceiling or maximum) temperatures, and this iteration process try to solve this problem by calculting L and U for recalculted Tb and Tc. In the process above To is optimum temperature. ... View more

It will be something like this:   data temp; k=(Tc-To)/(To-Tb); l=(0.05**2)*(To-Tb)*((Tc-To)**k); array L{i+1}=l/(((Tc-Tb)**(k+1))*((1-L{i}**k)); do i=0 to 10 by 1; end; run; The error in log still occured: 269 data temp; 270 k=(Tc-To)/(To-Tb); 271 l=(0.05**2)*(To-Tb)*((Tc-To)**k); 272 array L{i+1}=l/(((Tc-Tb)**(k+1))*((1-L{i}**k)); - 124 - 22 76 ERROR 124-185: The variable L has already been defined. ERROR 22-322: Syntax error, expecting one of the following: an integer constant, *. ERROR 76-322: Syntax error, statement will be ignored. 273 do i=0 to 10 by 1; 274 end; 275 run; NOTE: The SAS System stopped processing this step because of errors. WARNING: The data set WORK.TEMP may be incomplete. When this step was stopped there were 0 observations and 6 variables. WARNING: Data set WORK.TEMP was not replaced because this step was stopped. NOTE: DATA statement used (Total process time): real time 0.00 seconds cpu time 0.01 seconds When you said to assign values is such as initial values? Like L=0 ....... Could you help how to write this code?   ... View more

176 data temp; 177 k=(Tc-To)/(To-Tb); 178 l=(0.05**2)*(To-Tb)*((Tc-To)**k); 179 do i=0 to 10; 180 L[i+1]=l/(((Tc-Tb)**(k+1))*((1-L[i])**k)); ERROR: Undeclared array referenced: l. ERROR: Undeclared array referenced: l. ERROR: Variable l has not been declared as an array. ERROR: Variable l has not been declared as an array. 181 U[i+1]=(l/(((Tc-Tb)**(k+1))*((1-U[i])))**(1/k); - 79 ERROR: Undeclared array referenced: U. ERROR: Undeclared array referenced: U. ERROR: Variable U has not been declared as an array. ERROR 79-322: Expecting a ). 182 output; ERROR: Variable U has not been declared as an array. 183 end; I'm sorry, but I forgot to share the SAS log. Thanks PaigeMiler.   ... View more