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| Water Requirement Satisfaction Index (WRSI) -- Central America        |
|                                                                       |
| (updated: April 2003)                                                 |
|                                                                       |
| The spatially explicit water requirement satisfaction index (WRSI) is |
| an indicator of crop performance based on the availability of water   |
| to the crop during a growing season. FAO studies (Doorenbos and       |
| Pruitt, 1977) have shown that WRSI can be related to crop production  |
| using a linear yield-reduction function specific to a crop. More      |
| recently, Verdin and Klaver (2002) and Senay and Verdin (2003)        |
| demonstrated a regional implementation of WRSI in a grid cell based   |
| modeling environment.\                                                |
| \                                                                     |
| WRSI for a season is based on the water supply and demand a crop      |
| experiences during a growing season. It is calculated as the ratio of |
| seasonal actual evapotranspiration (AET) to the seasonal crop water   |
| requirement (WR):                                                     |
|                                                                       |
| WRSI = (AET / WR) \* 100.                                             |
|                                                                       |
| WR is calculated from the Penman-Monteith potential                   |
| evapotranspiration (PET) using the crop coefficient (Kc) to adjust    |
| for the growth stage of the crop:                                     |
|                                                                       |
| WR = PET \* KC.                                                       |
|                                                                       |
| AET represents the actual (as opposed to the potential) amount of     |
| water withdrawn from the soil water reservoir (\"bucket\"). Whenever  |
| the soil water content is above the maximum allowable depletion (MAD) |
| level (based on crop type), the AET will remain the same as WR, i.e., |
| no water stress. But when the soil water level is below the MAD       |
| level, the AET will be lower than WR in proportion to the remaining   |
| soil water content.\                                                  |
| \                                                                     |
| The soil water content is obtained through a simple mass balance      |
| equation where the level of soil water is monitored in a bucket       |
| defined by the water holding capacity (WHC) of the soil and the crop  |
| root depth, i.e.,                                                     |
|                                                                       |
| SWi = SWi-1 + PPTi - AETi                                             |
|                                                                       |
| where SW is soil water content, PPT is precipitation, and i is the    |
| time step index.\                                                     |
| \                                                                     |
| The most important inputs to the model are precipitation and          |
| potential evapotranspiration (PET). FEWS NET at the USGS calculates   |
| daily PET values for Central America at 1.0-degree resolution from    |
| 6-hourly numerical meteorological model output using the              |
| Penman-Monteith equation (Shuttleworth, 1992; Verdin and Klaver,      |
| 2002). Interpolated rain gauge data for Central America are obtained  |
| from NOAA at 0.1-degree (\~10 km) spatial resolution. In addition,    |
| the WRSI model uses relevant soil information from the FAO (1988)     |
| digital soils map and topographical parameters from Digital Elevation |
| Model (DEM) derived data                                              |
| ([HYDRO-1K](http://edcdaac.usgs.gov/gtopo30/hydro/africa.html), Gesch |
| et al. (1999)).\                                                      |
| \                                                                     |
| WRSI calculation requires a                                           |
| [start-of-season](http://edcw2                                        |
| ks21.cr.usgs.gov/adds/centralamerica/readme/sos_readme_amcentral.doc) |
| time (SOS) and end-of-season time (EOS) for each modeling grid-cell.  |
| Maps of these two variables are particularly useful in defining the   |
| spatial variation of the timing of the growing season and,            |
| consequently, the crop coefficient function, which defines the crop   |
| water use pattern of crops. The model determines the SOS using        |
| onset-of-rains based on simple precipitation accounting. The          |
| onset-of-rains is determined using a threshold amount and             |
| distribution of rainfall received in three consecutive dekads. SOS is |
| established when there is at least 25 mm of rainfall in one dekad     |
| followed by a total of at least 20 mm of rainfall in the next two     |
| consecutive decades. The length of growing period (LGP) for each      |
| pixel is determined by the crop variety. Generally, maize (corn) or   |
| beans with defined LGP are modeled for Central America. However, the  |
| WRSI model is capable of simulating different crop types whose        |
| seasonal water use pattern has been published in the form of a crop   |
| coefficient. Such crops include maize, sorghum, millet, wheat, etc.\  |
| \                                                                     |
| At the end of the crop growth cycle, or up to a certain dekad in the  |
| cycle, the sum of total AET and total WR are used to calculate WRSI   |
| in a Geographic Information System (GIS) environment at 0.1 degree    |
| (about 10 km) spatial resolution. A case of \"no deficit\" will       |
| result in a WRSI value of 100, which corresponds to the absence of    |
| yield reduction related to water deficit. A seasonal WRSI value less  |
| than 50 is regarded as a crop failure condition (Smith, 1992).\       |
| \                                                                     |
| Yield reduction estimates based on WRSI contribute to food security   |
| preparedness and planning. As a monitoring tool, the crop performance |
| indicator can be assessed at the end of every 10-day period during    |
| the growing season. As an early warning tool, end-of-season crop      |
| performance can be estimated using long-term average meteorological   |
| data.\                                                                |
| \                                                                     |
| Due to the difference in the growing season, WRSI maps are generated  |
| and distributed on a region-by-region basis (e.g., Haiti, Central     |
| America, the Sahel West Africa, Southern Africa, Greater Horn of      |
| Africa regions). At the end of every dekad, two image products        |
| associated with the WRSI are produced and disseminated for the FEWS   |
| NET activity. The following paragraphs provide a brief description of |
| these products.                                                       |
|                                                                       |
| **1. Current WRSI**\                                                  |
| This map portrays WRSI values for a particular crop from the start of |
| the growing season until this time period. It is based on the actual  |
| estimates of meteorological data to-date. For example, if the         |
| cumulative crop water requirement up to this period was 200 mm and    |
| only 180 mm was supplied in the form of rainfall, the crop            |
| experienced a deficit of 20 mm during the period and thus the WRSI    |
| value will be ((180 / 200) \* 100 = 90.0 %). This approach is         |
| slightly different from the traditional FAO update where the          |
| cumulative supply-to-date is compared to the seasonal crop water      |
| requirement, instead of the requirement up to the current period.     |
| Note that, unlike the FAO update, the current WRSI can increase in    |
| value in the later part of the growing season if the demand (crop     |
| water requirement) and supply (rainfall) relationship becomes         |
| favorable.                                                            |
|                                                                       |
| **2. Extended WRSI**\                                                 |
| This is a forecast estimate of WRSI at the end of the growing season. |
| Long-term average climatological data are used to calculate WRSI for  |
| the period between the current dekad and the end-of-season. The       |
| calculation principles are the same as the \"Current WRSI\". This is  |
| also a deficit-based estimate of WRSI.\                               |
| \                                                                     |
| The long-term average PET and rainfall is extracted from FAO\'s       |
| (1961-1990) long-term average monthly data. Note that at the end of   |
| the growing season, only current-year PET and PPT are used as input.  |
|                                                                       |
| **Water Requirement Satisfaction Index Anomaly\                       |
| **The WRSI anomaly map shows the relative magnitude of the WRSI as a  |
| percentage of the median WRSI:\                                       |
| WRSI Anomaly (%) = (Current WRSI / Median WRSI) \* 100\               |
| where "Current WRSI" is actually the current WRSI that is extended to |
| the end of season, and "Median WRSI" is WRSI generated using the      |
| median rainfall and evapotranspiration data from IWMI (International  |
| Water Management Institute) data set (1961-1990).\                    |
| \                                                                     |
| Although site/region specific validation is important, the user may   |
| use this anomaly map as a semi-quantitative indicator of the          |
| performance of the crops in relation to the average condition. For    |
| example, a value close to 100 signifies that this year\'s crop        |
| performance is about average, while percentage above and below 100    |
| may indicate above and below average production forecasts,            |
| respectively.                                                         |
|                                                                       |
| **References:**\                                                      |
| Doorenbos J and W.O. Pruitt, 1977. Crop water requirements. FAO       |
| Irrigation and Drainage Paper No. 24. Food and Agricultural           |
| Organization of the United Nations, Rome, Italy, 144p.\               |
| \                                                                     |
| Gesch, D.B., Verdin, K.L., and Greenlee, S.K. (1999). New land        |
| surface digital elevation model covers the Earth. EOS, Transactions   |
| of the American Geophysical Union, v. 80, n. 6, pp. 69-70.            |
|                                                                       |
| Senay, G.B. and J. Verdin, 2003. Characterization of Yield Reduction  |
| in Ethiopia                                                           |
|                                                                       |
| Using a GIS-Based Crop Water Balance Model. Canadian Journal of       |
| Remote Sensing. Accepted pending revision                             |
|                                                                       |
| Shuttleworth J. (1992). Evaporation. Handbook of Hydrology, Maidment, |
| D. (ed.). McGraw-Hill: New York; 4.1-4.53.\                           |
| \                                                                     |
| Smith, M. (1992). Expert consultation on revision of FAO              |
| methodologies for crop water requirements. FAO, Rome, Publication     |
| 73.\                                                                  |
| \                                                                     |
| Verdin, J. and Klaver, R. (2002). Grid cell based crop water          |
| accounting for the famine early warning system. Hydrological          |
| Processes, 16: 1617-1630.\                                            |
| \                                                                     |
| Xie, P. and Arkin, P.A. (1997). A 17-year monthly analysis based on   |
| gauge observations, satellite estimates, and numerical model outputs. |
| Bulletin of the American Meteorological Society 78(11): 2539-58.      |
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