SAS Introduction - Mendota Ice Record

Doug Hemken

February 2019

Introduction

This example looks at the Mendota Lake ice records to illustrate what an ordinary analysis might look like using SAS.

Questions:

  1. When does the lake usually ice over? (average "ice in")
  2. When does the ice usually break up? (average "ice out")
  3. How long does ice fishing season last? (typical duration)
  4. Can we detect global warming? (is there a trend?) How does this affect our answers in questions 1 through 3?

The data are published by the Wisconsin State Climatology Office

Data Step

The first step to our analysis is to read the data into SAS format. This uses a "global statement", filename, to tell SAS where to find the data on the web, and a DATA step, a block of SAS code that reads and manipulates the data into a format suitable for analysis.

(Most of the DATA step details are about getting dates into a convenient form for analysis.)

filename ice url 
  "http://www.ssc.wisc.edu/~hemken/SASworkshops/data/Mendota2019.txt";

data MendotaIce; * Creating a data set;
    infile ice firstobs=2;
    input Winter $ Closed $ Opened $ Days;
    year=input(substr(winter,1,4), 4.)+1;

    if closed ne "" then close = 
    input(compress(closed||put(year-1, 4.0), '-', 's'), date9.);
    if opened ne "" then open = 
    input(compress(opened||put(year, 4.0), '-', 's'), date9.);

    icein = mdy(month(close),day(close), 1960);
    if month(close) in (1, 2, 3) then close = 
    intnx('year', close, 1, 'sameday');
    if month(close) in (11, 12) then icein = 
    intnx('year', icein, -1, 'sameday');

    if month(open) eq 12 then open = 
    intnx('year', open, -1, 'sameday');
    dur = open - close;
    iceout = icein + dur;

    format close open mmddyy10.;
    format icein iceout date5.;

    drop closed opened;
    run;

Here is what the first few observations look like. I have coded icein and iceout in "day of the year" format, so that 0 = 1Jan, 1 = 2Jan, -1 = 31Dec, etc.

   Obs  Winter   Days  year       close        open  icein  dur  iceout

     1  1852-53     .  1853           .  04/05/1853      .    .      . 
     2  1853-54     .  1854  12/27/1853           .  27DEC    .      . 
     3  1854-55     .  1855           .           .      .    .      . 
     4  1855-56   118  1856  12/18/1855  04/14/1856  18DEC  118  14APR 
     5  1856-57   151  1857  12/06/1856  05/06/1857  06DEC  151  05MAY

Proc Step

With the data in SAS format, we can use various statistical PROCs to analyze the data.

Our first three questions can be answered with a single PROC MEANS.

proc means data=MendotaIce; * simple descriptive analysis;
    var days icein iceout;
    run;
                            The MEANS Procedure

Variable     N           Mean        Std Dev        Minimum        Maximum
--------------------------------------------------------------------------
Days       163    102.5092025     19.4987711     21.0000000    161.0000000
icein      172     -9.9883721     12.8700152    -39.0000000     63.0000000
iceout     170     88.1823529     23.3533884    -24.0000000    125.0000000
--------------------------------------------------------------------------

Over the last 150+ years, the average duration of ice cover has been 103 days, which gives us a substantial ice fishing season. The lake typically ices over 10 days before 1 January, or just as finals are ending. The ice usually breaks up around the 89th day of the year.

We could apply our date formats to interpret these results more easily.

                              icein    iceout

                              22DEC    29MAR

To see the distributions of the duration of ice cover, we can use a PROC step that produces graphs.

proc sgplot data=MendotaIce; * histograms;
    histogram days;
    run;

The SGPlot Procedure


Many procedures produce both tables and plots. To look at the distribution of ice out by month we could do this:

proc freq data=MendotaIce; * frequency, by month;
    tables iceout / plots=freqplot;
    format iceout monname.;
    run;
iceout Frequency Percent Cumulative
Frequency 		Cumulative
Percent
December 6 3.53 6 3.53
January 1 0.59 7 4.12
February 1 0.59 8 4.71
March 65 38.24 73 42.94
April 95 55.88 168 98.82
May 2 1.18 170 100.00
Frequency Missing = 4

Bar Chart of Frequencies for iceout


title "Days of Ice Cover";
title2 "Lake Mendota";

proc reg data=MendotaIce; * modeling yearly change in ice cover;
    model days = year;
    run; quit;
                             Days of Ice Cover
                               Lake Mendota

                             The REG Procedure
                               Model: MODEL1
                         Dependent Variable: Days 

          Number of Observations Read                        174
          Number of Observations Used                        163
          Number of Observations with Missing Values          11

                           Analysis of Variance
 
                                   Sum of          Mean
 Source                  DF       Squares        Square   F Value   Pr > F

 Model                    1         13111         13111     43.54   <.0001
 Error                  161         48482     301.13134                   
 Corrected Total        162         61593                                 

           Root MSE             17.35314    R-Square     0.2129
           Dependent Mean      102.50920    Adj R-Sq     0.2080
           Coeff Var            16.92837                       

                           Parameter Estimates
 
                        Parameter       Standard
   Variable     DF       Estimate          Error    t Value    Pr > |t|

   Intercept     1      471.70618       55.96971       8.43      <.0001
   year          1       -0.19060        0.02889      -6.60      <.0001
title;

data recentered;
    set mendotaice;
    yearc = year-2019;
    run;

proc reg data=recentered; * modeling yearly change in ice cover;
    model iceout = yearc;
    where days ne .;
    run; quit;
Model: MODEL1
Dependent Variable: iceout

Number of Observations Read 163
Number of Observations Used 163

Analysis of Variance
Source DF Sum of
Squares 		Mean
Square 		F Value Pr > F
Model 1 2966.07226 2966.07226 24.81 <.0001
Error 161 19248 119.55014
Corrected Total 162 22214

Root MSE 10.93390 R-Square 0.1335
Dependent Mean 92.36196 Adj R-Sq 0.1281
Coeff Var 11.83810

Parameter Estimates
Variable DF Parameter
Estimate 		Standard
Error 		t Value Pr > |t|
Intercept 1 84.92797 1.72073 49.36 <.0001
yearc 1 -0.09066 0.01820 -4.98 <.0001


Model: MODEL1
Dependent Variable: iceout

Panel of fit diagnostics for iceout.


Scatter plot of residuals by yearc for iceout.


Scatterplot of iceout by yearc overlaid with the fit line, a 95% confidence band and lower and upper 95% prediction limits.


2          data _null_;
3           mu=86;
4           ucl = mu + 1.96*10.86;
5           lcl = mu - 1.96*10.86;
6           put mu date.;
7           put lcl date.;
8           put ucl date.;
9           run;

27MAR60
05MAR60
17APR60
NOTE: DATA statement used (Total process time):
      real time           0.00 seconds
      cpu time            0.00 seconds
      

                                                                          1
                                           09:44 Tuesday, February 26, 2019

                             The REG Procedure
                               Model: MODEL1
                        Dependent Variable: iceout 

                  Number of Observations Read         163
                  Number of Observations Used         163

                           Analysis of Variance
 
                                   Sum of          Mean
 Source                  DF       Squares        Square   F Value   Pr > F

 Model                    1    2966.07226    2966.07226     24.81   <.0001
 Error                  161         19248     119.55014                   
 Corrected Total        162         22214                                 

           Root MSE             10.93390    R-Square     0.1335
           Dependent Mean       92.36196    Adj R-Sq     0.1281
           Coeff Var            11.83810                       

                           Parameter Estimates
 
                        Parameter       Standard
   Variable     DF       Estimate          Error    t Value    Pr > |t|

   Intercept     1       84.92797        1.72073      49.36      <.0001
   yearc         1       -0.09066        0.01820      -4.98      <.0001
proc reg data=recentered; * modeling yearly change in ice cover;
    model open = yearc;
    where days ne .;
    run; quit;
                                                                          1
                                           09:44 Tuesday, February 26, 2019

                             The REG Procedure
                               Model: MODEL1
                        Dependent Variable: iceout 

                  Number of Observations Read         163
                  Number of Observations Used         163

                           Analysis of Variance
 
                                   Sum of          Mean
 Source                  DF       Squares        Square   F Value   Pr > F

 Model                    1    2966.07226    2966.07226     24.81   <.0001
 Error                  161         19248     119.55014                   
 Corrected Total        162         22214                                 

           Root MSE             10.93390    R-Square     0.1335
           Dependent Mean       92.36196    Adj R-Sq     0.1281
           Coeff Var            11.83810                       

                           Parameter Estimates
 
                        Parameter       Standard
   Variable     DF       Estimate          Error    t Value    Pr > |t|

   Intercept     1       84.92797        1.72073      49.36      <.0001
   yearc         1       -0.09066        0.01820      -4.98      <.0001
 
                                                                           
 
                             The REG Procedure
                               Model: MODEL1
                         Dependent Variable: open 

                  Number of Observations Read         163
                  Number of Observations Used         163

                           Analysis of Variance
 
                                   Sum of          Mean
 Source                  DF       Squares        Square   F Value   Pr > F

 Model                    1   48118519693   48118519693   4.009E8   <.0001
 Error                  161         19325     120.02840                   
 Corrected Total        162   48118539017                                 

           Root MSE             10.95575    R-Square     1.0000
           Dependent Mean    -8307.74233    Adj R-Sq     1.0000
           Coeff Var            -0.13187                       

                           Parameter Estimates
 
                        Parameter       Standard
   Variable     DF       Estimate          Error    t Value    Pr > |t|

   Intercept     1          21635        1.72417    12547.9      <.0001
   yearc         1      365.15186        0.01824    20022.3      <.0001
2          data _null_;
3           mu=20540;
4           ucl = mu + 1.96*10.88;
5           lcl = mu - 1.96*10.88;
6           put mu date9.;
7           put lcl date.;
8           put ucl date.;
9           run;

27MAR2016
05MAR16
17APR16
NOTE: DATA statement used (Total process time):
      real time           0.00 seconds
      cpu time            0.00 seconds
      

                                                                          1
                                           09:44 Tuesday, February 26, 2019

                             The REG Procedure
                               Model: MODEL1
                        Dependent Variable: iceout 

                  Number of Observations Read         163
                  Number of Observations Used         163

                           Analysis of Variance
 
                                   Sum of          Mean
 Source                  DF       Squares        Square   F Value   Pr > F

 Model                    1    2966.07226    2966.07226     24.81   <.0001
 Error                  161         19248     119.55014                   
 Corrected Total        162         22214                                 

           Root MSE             10.93390    R-Square     0.1335
           Dependent Mean       92.36196    Adj R-Sq     0.1281
           Coeff Var            11.83810                       

                           Parameter Estimates
 
                        Parameter       Standard
   Variable     DF       Estimate          Error    t Value    Pr > |t|

   Intercept     1       84.92797        1.72073      49.36      <.0001
   yearc         1       -0.09066        0.01820      -4.98      <.0001