cw25 (about 1 month after silking time): Table valid for eastern states (IL, IN, IA, MN, MO, WI)
Given a particular AI, the number of districts in eastern states (1980 to 1999) with positive yield deviation and the total.
‡ (†) indicates percentage is significantly (at the 0.05 probability level) higher (lower) than the unconditional percentage of cases above trend (62.5%).

cw21 (about silking time): Table valid for eastern states (IL, IN, IA, MN, MO, WI)
Given a particular AI, the number of districts in eastern states (1980 to 1999) with positive yield deviation and the total.
‡ (†) indicates percentage is significantly (at the 0.05 probability level) higher (lower) than the unconditional percentage of cases above trend (62.5%).

cw17 (about 1 month before silking): Table valid for eastern states (IL, IN, IA, MN, MO, WI)
Given a particular AI, the number of districts in eastern states (1980 to 1999) with negative yield deviation, with positive yield deviation, and altogether.
‡ (†) indicates percentage is significantly (at the 0.05 probability level) higher (lower) than the unconditional percentage of cases above trend (62.5%).

AI	Below	Above	Total	% Cases above Trend
-8 to -6	2	4	6		66.7
-6 to -4	67	36	103	†	35.0
-4 to -2	76	72	148	†	48.6
-2 to 0	86	156	242		64.5
0 to 2	71	193	264	‡	73.1
2 to 4	42	99	141	‡	70.2
4 to 6	10	30	40		75.0
6 to 8	2	4	6		66.7

cw13: Table valid for eastern states (IL, IN, IA, MN, MO, WI)
Given a particular AI, the number of districts in eastern states (1980 to 1999) with negative yield deviation, with positive yield deviation, and altogether.
‡ (†) indicates percentage is significantly (at the 0.05 probability level) higher (lower) than the unconditional percentage of cases above trend (62.5%).

AI	2 months before silking (week 13)
	Below	Above	Total	% cases above trend
-6 to -4	9	11	20		55.0
-4 to -2	45	77	122		63.1
-2 to 0	135	189	324	†	58.3
0 to 2	120	267	387	‡	69.0
2 to 4	47	50	97	†	51.5

Studies done with simulation models (e.g. Duchon 1986) require numerous details about crop management and environment, so for yield estimation over a large area, the regression approach has been more widely used (Walker 1989). Because of the large influence of moisture on crops, and the harmfulness of limited moisture, it is natural to relate crop yield to the occurrence and severity of drought, which is usually expressed in terms of an index. Taylor (personal communication 2002) explains, "in order for index data to be a useful indicator for risk assessment, it must be simply derived and indicative of a result. The index concept is not intended to be rigorously predictive, but is expected to provide reliable assessment of risk and detection of risk change."

Byun and Wilhite (1999) provide a summary of some drought indexes to preface their discussion of the advantages and disadvantages of the indexes.
"Most drought indexes are based on meteorological or hydrological variables. They include the Palmer Drought Severity Index (PDSI; Palmer 1965), Rainfall Anomaly Index (RAI; van Rooy 1965), deciles (Gibbs and Maher 1967), Crop Moisture Index (CMI; Palmer 1968), Bhalme and Mooly Drought Index (BMDI; Bhalme and Mooly 1980), Surface Water Supply Index (SWSI; Shafer and Dezman 1982), National Rainfall Index (RI; Gommes and Petrassi 1994), Standardized Precipitation Index (SPI; McKee et. al. 1993, 1995), and Reclamation Drought Index (RDI; Weghorst 1996). The Soil Moisture Drought Index (SMDI; Hollinger et. al. 1993) and Crop-Specific Drought Index (CSDI; Meyer et. al. 1993; Meyer and Hubbard 1995) appeared after CMI. ....Of all the indexes, the PDSI is still the most widely used and recognized index on an operational basis" (Byun and Wilhite 1999).

The popularity of the PDSI and the CMI promotes uses, such as crop assessment, for which they were not intended (Meyer et. al. 1993a), and in some situations prove to be quite unreliable (Meyer et. al. 1991). Others have examined various yield and water availability relationships on a monthly scale (eg., Thompson 1986; Walker 1989; Stephens et. al. 1994; Harouna and Carlson 1994), but crop development, at some points in the life cycle, can advance to the next stage in just several days, so a monthly time scale can smooth the importance of the variable or split a growth stage into two pieces.� A smaller time scale is likely to be better suited when dealing with crop growth and yield.

Shaw (1983) and Meyer et. al. (1993a, b) used submonthly indexes for crop assessment and reported satisfactory results, but their methods involved fairly direct evaluations of evapotranspiration. Because some data for the indexes' input parameters are not readily available (eg., pan evaporation; net radiation, soil water), the evaluation of actual and potential evapotranspiration for the indexes is not easy to assess in near real-time, so an alternate method is presented.

With consideration to Shaw’s (1983) stress index, air temperature plays a large role in evaporation from plants, and precipitation is a major factor for the availability of moisture, so it was felt that they alone could also be used in determining water availability and the resulting amount of yield a corn crop will produce. In a general sense, an average amount of precipitation during the growing season (assuming a sufficient initial amount) will provide sufficient moisture for an average corn crop. However, drier and warmer than usual, which is established as high aridity below, means the corn crop will tend to be stressed, which according to Shaw’s (1983) stress yield relationship will result in a lower yield.

Definition of the Aridity Index
Harouna and Carlson (1994) used monthly precipitation’s departure from normal, a technique discussed by Barring and Hulme (1991), and combined it with the monthly maximum temperature’s departure from normal, applied in the same manner, into an aridity index. However, here the aridity index (Equation 1; hereafter referred to as AI) was modified so that it was a combination of weekly maximum temperature’s departure from normal (Equation 2) and the weekly precipitation’s departure from normal (Equation 3).
The index of aridity for each climate week(i) and year(j) is given by:
(climate week 1 begins March 1 for any given year)

    AI_ij = T' – P'      (1)

where

         T - Tbar
T' = -----------      (2)
              S_t

         P - Pbar
P' = -----------      (3)
              S_p

T'     is the standardized weekly maximum temperature
T      is the weekly maximum temperature
Tbar is the weekly mean maximum temperature over all years
S_t    is the standard deviation of the maximum temperature over all years

P'     is the standardized weekly precipitation
P      is the weekly precipitation
Pbar is the weekly mean precipitation over all years
S_p    is the standard deviation of the precipitation over all years

AI equally weights the contribution of temperature and precipitation and generally gives positive (negative) values when the weather is warm and dry (cool and wet).
However, it was felt beneficial for the general public to have negative yield deviation correspond to negative AI values. Warmer and drier than normal weather tends to have a negative effect on the yield. Positive AI, as defined above indicated warmer and drier than normal, so AIs were multiplied by –1 such that results are presented so that an AI less than zero will indicate warmer and drier than normal. This results in a slope that generally appears positive when yield deviation is plotted against AI and will allow users to associate AIs less than zero with a better chance for poor yield.

Shaw (1983) dealt with the yield’s response to the timing of stress by implementing a weighting scheme. Silking time is the most sensitive to stress, so Shaw (1983) accordingly weighted stress during silking the most heavily and reduced the weight as the 5-day periods before and after silking became farther away. Shaw’s (1983) yield prediction method starts with an initial potential yield and subtracts from it as stress accumulates. Thus, yield loss can be assessed during the season by noting the sum of stress values at the particular time. At the end of the season, the summed stress values gives a seasonal stress index. These concepts, weighting for phenology and summing the index throughout the season, were incorporated here with the weekly AI.

A seasonal AI-yield relationship is different from a seasonal stress-yield relationship because instead of starting with a potential yield and subtracting for stress, the AI method starts with a predicted yield extrapolated from trend, and the initial yield prediction deviates as the weekly AI sum (Equation 5) deviates from zero. The weights applied to each week’s AI were adopted from Shaw (1983) assuming the critical times for temperature and precipitation deviation from normal are approximately the same as the critical times for stress. The “weighted AI” AIw_ij is computed from Equation 1 by:
for all j and i = 11, 12, ..., 27        AIw_ij = k_i AI_ij           (4)

where k_i is the factor used to adjust for crop phenology at week i (Table). The seasonal progression (AIw to date) used for public information is computed from Equation 4 as:
at week i,                 mid-seasonal AIw = ΣAIw_i       (5)

Climate Week (i)	Begin Date	Weighting Factor (ki)
11	5/10	-0.5
12	5/17	-0.5
13	5/24	-0.5
14	5/31	0.5
15	6/7	0.5
16	6/14	0.5
17	6/21	1.0
18	6/28	1.0
19	7/5	1.0
20	7/12	1.0
21	7/19	2.2
22	7/26	1.6
23	8/2	1.3
24	8/9	1.3
25	8/16	1.3
26	8/23	1.0
27	8/30	0.75

AI Definition Error
There are some issues with the AI definition. One issue is the possibility of certain combinations of extreme weather weeks causing the AI to be near neutral at any particular time. The extreme weather could quite likely result in a fairly large below trend YLD, but if opposite weather occurred for enough weeks, the resulting AI value would not indicate the drastic negative YLD. For example, if July was arid, and August was equally cool and wet, then AI would be near zero, but the crop did poorly because of the July conditions. The method, as it stands now, allows the AI to move back toward zero even though the negative deviation may be permanent. In other words, the crop’s ability to recover from aridity or flood is quite limited, but the AI method does not account for this limitation. Another consideration in regard to the defining equation of AI is the possibility of AI being near zero when a week's weather is wet and warm or cool and dry. It was assumed these conditions would have approximately the same effects as average conditions. Warm would indicate higher transpiration, but wet would mean precipitation would be sufficient to sustain the higher transpiration. Similarly, cool would indicate lower transpiration, so no rain would not be harmful. Finally, normalizing a precipitation distribution that is not normal may also influence results.

Timing and Appropriate Weighting
Another thing to consider is the way silking time was generalized here. All weighting was applied with respect to having main silking occurring during climate week 21 and all weighting was applied to all districts equally. In IA, there is a good chance silking will occur in or near week 21, but silking may happen at different times in other places. If enough timely information regarding silking dates could be obtained during the course of the period, it might be possible to adjust weighting with each weekly processing of AI as conditions warrant.

Other Error Sources
There are other possible sources of error. For high aridity, irrigated corn may do well and keep the total yield relatively higher even though AI is quite low. Thus, the total yield in the eastern states may have contributions from irrigated corn, which may have influenced the yield deviation used here for the eastern states. Meyer et. al. (1993a) acknowledge that soil quality, hybrid type, and damaging elements such as insects, disease, hail, and wind impact yield and may be sources of error. Thompson (1986) studied the effects of climate change on the upward trend in corn yield, and thus had to separate the influence of weather from the influence of greater fertilization, improved genetics, improved pest control, and improved management.

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