# Presentation: 305863

## Computing the Monthly Palmer Drought Index on a Weekly Basis

**Richard R. Heim Jr.**
*NOAA/NESDIS/National Climatic Data Center*
*Asheville, North Carolina*
- USDM Workshop
- Washington, D.C., October 2005

## Statement of the Problem

**Palmer developed his drought index using monthly data**
**Monthly Palmer Drought Index (PDI or PMDI) has century-scale historical perspective**
**Timeliness of monthly PDI for operational drought monitoring is an issue**
**Weekly PDI more timely, but historical record / historical perspective shorter (back to early 1970s)**
**Weekly PDI & monthly PDI sometimes inconsistent when used operationally**

## February 2005

- CPC Weekly PDI,
- Feb. 26, 2005

- NCDC Monthly PDI,
- End of Feb. 2005

## Goal

**April 2002 USDM Forum:  We need to address the issue of differences between the operational weekly PDI and operational monthly PDI**
**How?  --  Compute a monthly PDI operationally before the end of the month**
**Issue --  How to estimate the monthly temperature and precipitation Palmer input before the month is over**
**Current forecasting technology does not include predictions a month in advance for daily temperature and precipitation amount at the resolution needed to compute the PDI for this purpose.**

## Goal

**Compare 3 potential estimation methods for the unknown portion of the month**
**Persistence** of the values for day 1 through X to the end of the month
**Moving Window**:  the values for day 1 through X of current month combined with the values for day Y through end of previous month
**Normals** used for day X+1 through the end of the month
**The successful method should yield weekly PDI values that result in a reasonable transition from the monthly PDI values that existed at the beginning of the month (i.e., at the end of the previous month) to the monthly PDI values that exist at the end of the month.**

## Data

**NCDC Monthly climate division temperature & precipitation data – historical**
**CPC 1000-day climate division file – operational daily**
**1971-2000 daily divisional normals – the ****Normals**** methodology **
**Monthly temperature & precipitation computed from the CPC daily values (& normals for ****Normals**** methodology)**
**Monthly PDI computed from the monthly temperature & precipitation values**

## July 2003 – Test Case

- CPC Weekly PDI,
- July 26, 2003

- NCDC Monthly PDI

- End
- Of
- July
- 2003

- End
- Of
- June
- 2003

## Procedure

**Analyzed July 2003 climate division data**
**Monthly PDI values for June 2003 (June 30) and July 2003 (July 31) computed by NCDC used as “TRUTH”**
**Weekly PDI values computed for July 5, 12, 19, 26, 2003 for the 3 estimation methods ( “TEST”) from daily data to correspond to the weeks PDI was computed by CPC**
**The 3 estimation methods were evaluated using these comparison statistics:**
- Computed absolute value of the differences between TEST & TRUTH
- Mean and variance of the absolute value of the differences measured the degree of closeness between the TEST & TRUTH values
- Pearson correlation coefficient measured their spatial / geographic comparability

## PDI - July Weekly Methods vs. June Monthly

| Technique | July 5 | July 12 | July 19 | July 26 | July 31 |
| --- | --- | --- | --- | --- | --- |
| 
Normals | 0.32
0.106
0.982 | 0.56
0.387
0.944 | 0.65
0.406
0.936 | 0.75
0.513
0.922 | 0.79
0.522
0.919 |
| 
Window | 0.87
0.359
0.954 | 0.78
0.481
0.939 | 0.68
0.411
0.935 | 0.81
0.547
0.913 | 0.79
0.522
0.919 |
| 
Persistence | 1.72
1.989
0.822 | 1.32
1.312
0.837 | 1.01
0.789
0.885 | 0.88
0.643
0.905 | 0.79
0.522
0.919 |
| 
CPC Weekly | 1.07
0.881
0.879 | 1.19
1.011
0.860 | 1.35
1.196
0.848 | 1.47
1.289
0.826 | 
NA |

- Top: Mean Abs. Diff.  -  Middle: Variance of Abs. Diff.  -
- Bottom: Correlation Coefficient of Abs. Diff.

## Comparison Results:  June Monthly

**vs. July Weekly PDI**

**Normals**** methodology has smaller mean & variance of absolute diff., and higher correlations, than the ****Window**** & ****Persistence**** methods **
**Normals**** methodology for July weeks has steadily increasing departures from end of June monthly values as the weeks progress**
**Conclusion:  ****Normals**** methodology gives results that represent the best transition from the drought and wet spell conditions of the previous month**

## PDI - July Weekly Methods vs. July Monthly

| Technique | July 5 | July 12 | July 19 | July 26 | July 31 |
| --- | --- | --- | --- | --- | --- |
| 
Normals | 0.70
0.365
0.942 | 0.51
0.193
0.974 | 0.36
0.104
0.985 | 0.16
0.023
0.997 | 0
0
1.0 |
| 
Window | 1.13
0.832
0.890 | 0.83
0.475
0.939 | 0.62
0.289
0.955 | 0.24
0.062
0.992 | 0
0
1.0 |
| 
Persistence | 1.38
1.680
0.872 | 0.82
0.463
0.952 | 0.46
0.165
0.978 | 0.20
0.035
0.996 | 0
0
1.0 |
| 
CPC Weekly | 1.11
1.086
0.859 | 0.95
0.832
0.901 | 1.03
0.914
0.908 | 1.05
0.812
0.917 | 
NA |

- Top: Mean Abs. Diff.  -  Middle: Variance of Abs. Diff.  -
- Bottom: Correlation Coefficient of Abs. Diff.

## Comparison Results:  July End-of-Month

**vs. July Weekly PDI**

**All 3 methodologies have decreasing departures for every week as the month progresses, with all 3 converging to the same (end-of-month) values**** **
**Normals**** methodology has smaller mean & variance of absolute diff., and higher correlations, than the ****Window**** & ****Persistence**** methods, for every week **
**Conclusion:  ****Normals**** methodology gives results that represent the best transition to the monthly drought and wet spell conditions at the end of the current month**

## Spatial Variability of the Mean Abs. Diff.

**July Weekly vs End of June**

- Normals

- Window

- Persistence

- Normals method performed better in
- areas experiencing intensifying wet or
- dry conditions

## Spatial Variability of the Mean Abs. Diff.

**July Weekly vs End of July**

- Normals

- Window

- Persistence

- Normals method has best
- overall performance

## Time Series Plots

- For each of these 3 divisions, in all weeks but one the Normals method yields a better value.

## http://www.ncdc.noaa.gov/oa/climate/monitoring/drought/mw/

- June 2005

- July 2005

## Conclusions

- The Normals methodology produces results which are more reasonable than a Persistence or moving Window approach for estimating the Palmer Drought Index for a month before the month is over.
- Smaller “error estimates”
- Better correlations
- A monthly Palmer Drought Index computed on a weekly (or even daily) basis, using normal temperature and precipitation to estimate the weather for the rest of the month, is useful for monitoring drought on an operational basis.

##      Thank You!

**http://www.ncdc.noaa.gov/oa/climate/monitoring/drought/mw/**

- Heim, R.R., Jr., 2005: Computing the monthly Palmer Drought Index on a weekly basis: A case study comparing data estimation techniques.
*Geophys. Res. Lett.*, **32**, No. 6, L06401, 18 March 2005.

## Slide 19