This document briefly explains how predicted livestock mortality index is derived. First, we explain how and why we have separate index-based livestock insurance (IBLI) contracts across Marsabit. We then describe the forage availability proxy we use, Normalized Difference Vegetation Index (NDVI) and then explain how predicted livestock mortality index is constructed based on NDVI

International Livestock Research Institute

CGSpace (CGIAR)

Derive Predicted Livestock Mortality Index        This document briefly explains how predicted livestock mortality index is derived1.  First, we explain how and why we have separate index-based livestock insurance (IBLI) contracts across Marsabit.  We then describe the forage availability proxy we use, Normalized Difference Vegetation Index (NDVI) and then explain how predicted livestock mortality index is constructed based on NDVI.    1. The division of Marsabit: 2 Insurance Contract Areas and 5 Predicted Livestock Mortality Index Areas       IBLI divides Marsabit area as shown in Figure 1.  Upper and Lower Marsabit have different insurance contracts.  By this we mean that both Upper and Lower Marsabit contracts are modeled and priced using a separate response function which determines the relationship between constructed NDVI variables and livestock mortality as explained below.  This split was made due to substantial differences in agro-ecology, herd compositions and climate patterns between these two regions.        IBLI further divides Marsabit into 5 divisions, each of which has its own predicted livestock mortality index. That is, that the average NDVI reading is taken at the division level plugged into the same response function for divisions in Upper Marsabit (North Horr and Maikona) and those in Lower Marsabit (Loiyangalani, Laisamis and Central)   This division into 5 was chosen in order to strike a compromise between increasing localized index precision by using more disaggregated NDVI values and having fewer indexing areas to reduce administrative logistics and account for the wide area pastoralists commonly graze.                                                    1 See Chantrat et al (2009) for the detail.   Upper Marsabit MaikonaNorth Horr    Lower Marsabit Central and GadamojiLaisamisLoiyangalani KARGISHURAMAIKONABUBISATURBIILLERETGALASSABARETKOYADARADENORTH HORRDUKANAEL GADEKORRKURUGUMBALESALAISAMISEL-HADIFUROLEKALACHAHAFAREGASHURRI HILLSLOIYANGALANIKURUNGULONTOLIOARAPALLOGOLOGOQILTAMT. KULALMOITEGUDAS/SORIADIKARAREIRIRNGURUNITLARACHIKAMBOYESOUTH HORR(MARSA)LONYORIPICHAUSONGAMERILLEILLAUT(MARSABIT)HULAHULAMAJENGO(MARSABIT)OGUCHOOLTUROTJALDESAKITURUNIDIRIB GOMBOJIRIMESAGANTE Figure 1. 2 Insurance contract areas and 5 predicted livestock mortality index areas         2. NDVI        The Normalized Difference Vegetation Index (NDVI) is a satellite derived indicator of the amount and vigor of vegetation. The magnitude of NDVI is related to the level of photosynthetic activity in the observed vegetation. Images of NDVI are sometimes referred to as "greenness maps" since they represent the vegetative vigor of plants. In general, high values of NDVI indicate greater vigor and amounts of vegetations.  The NDVI data are available at the resolution of 8.0×  8.0 km. Since the late 1980's, the Famine Early Warning System (FEWS) has used AVHRR data2 to produce dekadal (10-day) composite NDVI images of Africa, and has built a valuable archive of these data from June 1981 to present, which are available in real time.  Figure 2 shows NDVI in Marsabit in the 1st dekad of February 2009.                                                  2 NDVI is derived from data collected by National Oceanic and Atmospheric Administration (NOAA) satellites, and processed by the Global Inventory Monitoring and Modeling Studies group (GIMMS) at the National Aeronautical and Space Administration (NASA).   LegendNDVI<VALUE>0 - 0.10.1 - 0.20.2 - 0.30.3 - 0.40.4 - 0.50.5 - 0.60.6 - 0.70.7 - 0.80.8 - 0.90.9 - 1  Figure 2. NDVI in Marsabit in 1st dekad of January 2010  3. ZNDVI  In order to take into account the differences in weather impact on vegetation, geographic attributes and resources (soil, vegetation type and topography), we use standardized NDVI, zndvi  for any pixel i of dekadal d in year t :      ( )( )idtdidtdidtidtndvindviEndvizndviσ−=      where idtndvi  is the image of NDVI for pixel i for dekad d of year t, ( )idtd ndviE  is the long-term mean of NDVI values for dekad d of pixel i taken over 1982-2009 and ( )idtd ndviσ  is the long-term standard deviation of NDVI values for dekad d of pixel i taken over 1982-2009.  Positive (negative) idtzndvi  represents relatively better (worse) vegetation condition relative to the long-term mean driven by climate.  Figure 3 shows ZNDVI in Marsabit in the 1st dekad of January 2010.  Figure 2 shows that most of Marsabit was very dry in the 1st decade of January but Figure 3 reveals that, at least in the Northern part of Marsabit, it was greener compared to the same dekad in previous years.  Figure 4 shows time series of ZNDVI in North Horr from 2000 to 2010.     Zndvi<VALUE>< -1.75-1.75 - -1.25-1.25 - -0.75-0.75 - -0.25-0.25 - 0.250.25 - 0.750.75 - 1.251.25 - 1.75> 1.75  Figure 3. ZNDVI in Marsabit in 1st dekad of January 2010   Figure 4.  ZNDVI in North Horr from 2000 to 2009   4. Czndvi      To reasonably capture the cumulative impact of climate, we introduce the cumulative path of zndvi (e.g., Czndvi ) into the model. After investigating various cumulative variables with different periods and different ways of cumulating, we identify the following cumulative NDVI variables for inclusion.  Figure 5 shows time flow of insurance coverage periods and NDVI summation periods for the various variables.    An annual period is divided into 2 seasons: Long rain long dry (LRLD) season from March to September and short rain short dry (SRSD) season from October to February.  For LRLD insurance coverage, we capture NDVI in the previous SRSD and across the duration of the coverage LRLD.  Similarly, for SRSD insurance coverage, we capture NDVI in the previous LRLD and the SRSD.  Based on these insurance coverage periods and NDVI reading periods, we construct the following 4 types of cumulative ZNDVI variables:  Oct      Nov      Dec       Jan     Feb       Mar       Apr     May     Jun       Jul       Aug      SepLRLD seasonAccumulation process of zndvi∑−==MarOctzndvipreCzndvi,1,1 1_ττ ∑−==SeptOctzndviposCzndvi,3,1 1_ττ∑==SeptMarzndviMinCNzndvi,3,1)0,(ττ∑==SeptMarzndviMaxCPzndvi,3,1)0,(ττMar       Apr      May     Jun       Jul       Aug      Sep     Oct      Nov      Dec      Jan      FebAccumulation process of zndviSRSD season∑−==OctMarzndvipreCzndvi,1,1 1_ττ ∑−==FebMarzndviposCzndvi,3,1 1_ττ∑==FebOctzndviMinCNzndvi,3,1)0,(ττ∑==FebOctzndviMaxCPzndvi,3,1)0,(ττLRLD modelSRSD model Figure 5. Temporal structure of IBLI Contract  (Insurance coverage periods and NDVI reading periods)  1. Czndvi_pos = cumulative ZNDVI represents total cumulative effect of deviations of vegetation condition from normal that are accumulated since the previous rain season to the end of coverage season o ∑∈=sposTddss zndviposCzndvi _ where sposT   = October – September (March – February) if s = LRLD (SRSD).  2. Czndvi_pre = cumulative ZNDVI represents cumulative pre-condition of deviations of vegetation condition from normal accumulated since the previous rain season to the beginning of the coverage season. o ∑∈=spreTddss zndvipreCzndvi _ where spreT  = October – March (March – October) if s = LRLD (SRSD). 3. CNzndvi = cumulative of the negative ZNDVI represents cumulative effect of below normal vegetation condition that during the coverage season. o  ∑∈=sTddss zndviMinCNzndvi )0,(  wheresT  = March – September (October – February) if s = LRLD (SRSD).)  4. CPzndvi = cumulative of the positive ZNDVI represents cumulative effect of above normal vegetation condition during the coverage season.  o ∑∈=sTddss zndviMaxCPzndvi )0,(  wheresT  = March – September (October – February) if s = LRLD (SRSD).   Figure 6 shows Czndvi_pre and Czndvi_pos for Oct-Feb (SRSD) insurance period from 2000 to 2009.  As figure shows that 1) we start counting Czndvi in the beginning of March, 2) Czndvi_pre is determined in the end of 1st dekad of October, and 3) Czndiv_pos is determined in the end of February.  Short rain - Short dry Contract Window (March - February)North Horr - Historical Cumulative ZNDVI (2000-2009) -30-20-1001020301 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Dekad Number2000200120022003200420052006200720082009Czndvi_pre Czndvi_posMar            Apr              May             Jun             Jul               Aug             Sep              Oct          Nov              Dec             Jan             FebMar 6Mar 16Mar 26Apr 6Apr 16Apr 26May 6May 16May 26Jun 6Jun 16Jun 26Jul 6Jul 16Jul 26Aug 6Aug 16Aug 26Sep 6Sep 16Sep 26Oct 6Oct 16Oct 26Nov 6Nov16Nov 26Dec 6Dec 16Dec 26Jan 6Jan 16Jan 26Feb 6Feb 16Feb 26Mar 6Mar 16Mar 26Apr 6Apr 16Apr 26May 6May 16May 26Jun 6Jun 16Jun 26Jul 6Jul 16Jul 26Aug 6Aug 16Aug 26Sep 6Sep 16Sep 26Oct 6Oct 16Oct 26Nov 6Nov16Nov 26Dec 6Dec 16Dec 26Jan 6Jan 16Jan 26Feb 6Feb 16Feb 26Mar 6Mar 16Mar 26Apr 6Apr 16Apr 26May 6May 16May 26Jun 6Jun 16Jun 26Jul 6Jul 16Jul 26Aug 6Aug 16Aug 26Sep 6Sep 16Sep 26Oct 6Oct 16Oct 26Nov 6Nov16Nov 26Dec 6Dec 16Dec 26Jan 6Jan 16Jan 26Feb 6Feb 16Feb 26 Figure 6. Czndvi_pre and Czndvi_pos for Oct-Feb (SRSD)  insurance period from 2000 to 2009   5. Predicted Livestock Mortality Index In order to capture the difference in area-averaged mortality responses to climate (strictly speaking, to climate-driven vegetation condition) between moderate and severe climate outcome, we use the following regime switching model in estimating the relationship between Czndvi variables and livestock mortality:    ( ) lslsls ndviXMM 1111 )( ε+=            if 0_ ≥lsposCzndvi     (good-climate regime)   ( ) lslsls ndviXMM 2222 )( ε+=          if 0_ <lsposCzndvi      (bad-climate regime) where the cumulative zndvi  since last rain until the end of the season ( lsposCzndvi _ ) serves as an indicator of seasonal climate outcome to determine regime into which each season belong: either a good-climate regime or a bad one.  The estimation results which derive the predicted livestock mortality index from NDVI are as follows:     Upper Marsabit  o Predicted livestock mortality index for long rain – long dry coverage (M_LRLD):   M_LRLD = 0.0024 × Czndvi_pos if Czndvi_pos >= 0,   M_LRLD = (-0.0187 × Czndvi_pre) + (0.0019 × CNzndvi) + (-0.0064 × CPzndvi) if Czndvi_pos < 0,  o Predicted livestock mortality index for short rain – short dry coverage (M_SRSD):  M_SRSD = 0.0024 × Czndvi_pos if Czndvi_pos >= 0,   M_SRSD = (-0.0187 × Czndvi_pre) + (0.0019 × CNzndvi) + (-0.0064 × CPzndvi) + 0.0354 if Czndvi_pos < 0  Lower Marsabit o Predicted livestock mortality index for long rain – long dry coverage (M_LRLD):  M_LRLD =  (-0.0003 × Czndvi_pre) + (0.0087 × CNzndvi) + (0.0014 × CPzndvi) if Czndvi_pos >= 0  M_LRLD = (-0.0093 × Czndvi_pre) + (0.0117 × CNzndvi) + (-0.0111 × CPzndvi) if Czndvi_pos < 0  o Predicted livestock mortality index for short rain – short dry coverage (M_SRSD):  M_SRSD =  (-0.0003 × Czndvi_pre) + (0.0087 × CNzndvi) + (0.0014 × CPzndvi) + 0.0147 if Czndvi_pos >= 0  M_SRSD = (-0.0093 × Czndvi_pre) + (0.0117 × CNzndvi) + (-0.0111 × CPzndvi) + 0.0147 if Czndvi_pos < 0         Figure 7 shows the time series of predicted livestock mortality index for Oct-Feb (SRSD) insurance period from 2000 to 2009 in North Horr.  Note that the index was determined in the end of short dry season, the most right in the figure, and predicted mortality before the end of short dry season gives us only forecast on the index based on available NDVI data at that point of time.     Short rain - Short dry Contract Window (March - February)North Horr - Predicted Mortality Index (2000-2009) 0%5%10%15%20%25%30%35%40%45%50%1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Dekad Number2000200120022003200420052006200720082009  Figure 7. Forecast of predicted livestock mortality index  for Oct-Feb (SRSD) insurance period  from 2000 to 2009 in North Horr  6. Update on NDVI and Predicted Livestock Mortality Index  See Mortality Index Update page on http://www.ilri.org/ibli/  Reference  Chantarat, S., A. G. Mude, C. B. Barrett, and M. R. Carter (2009) “DESIGNING INDEX BASED LIVESTOCK INSURANCE FOR MANAGING ASSET RISK IN NORTHERN KENYA” Working Paper, Cornell University, July. Available at Papers page on http://www.ilri.org/ibli/  

Derive predicted livestock mortality index

29 March 2011 Derive Predicted Livestock Mortality Index        This document briefly explains how predicted livestock mortality index is derived1.  First, we explain how and why we have separate index-based livestock insurance (IBLI) contracts across Marsabit.  We then describe the forage availability proxy we use, Normalized Difference Vegetation Index (NDVI) and then explain how predicted livestock mortality index is constructed based on NDVI.    1. The division of Marsabit: 2 Insurance Contract Areas and 5 Predicted Livestock Mortality Index Areas       IBLI divides Marsabit area as shown in Figure 1.  Upper and Lower Marsabit have different insurance contracts.  By this we mean that both Upper and Lower Marsabit contracts are modeled and priced using a separate response function which determines the relationship between constructed NDVI variables and livestock mortality as explained below.  This split was made due to substantial differences in agro-ecology, herd compositions and climate patterns between these two regions.        IBLI further divides Marsabit into 5 divisions, each of which has its own predicted livestock mortality index. That is, that the average NDVI reading is taken at the division level plugged into the same response function for divisions in Upper Marsabit (North Horr and Maikona) and those in Lower Marsabit (Loiyangalani, Laisamis and Central)   This division into 5 was chosen in order to strike a compromise between increasing localized index precision by using more disaggregated NDVI values and having fewer indexing areas to reduce administrative logistics and account for the wide area pastoralists commonly graze.                                                    1 See Chantrat et al (2009) for the detail.   Upper Marsabit    Lower Marsabit   Figure 1. 2 Insurance contract areas and 5 predicted livestock mortality index areas         2. NDVI        The Normalized Difference Vegetation Index (NDVI) is a satellite derived indicator of the amount and vigor of vegetation. The magnitude of NDVI is related to the level of photosynthetic activity in the observed vegetation. Images of NDVI are sometimes referred to as "greenness maps" since they represent the vegetative vigor of plants. In general, high values of NDVI indicate greater vigor and amounts of vegetations.  The NDVI data are available at the resolution of 8.0×  8.0 km. Since the late 1980's, the Famine Early Warning System (FEWS) has used AVHRR data2 to produce dekadal (10-day) composite NDVI images of Africa, and has built a valuable archive of these data from June 1981 to present, which are available in real time.  Figure 2 shows NDVI in Marsabit in the 1st dekad of February 2009.  Point to Note:  As per the above paragraph, the NDVI response function was modeled based on AVHRR NDVI data.  The intention was then to use regularly available NDVI data to then generate the predicted livestock mortality indices.  However, in March 2010, the sensor producing AVHRR data began to deteriorate and has since then been offline.  In conjunction with scientists from the Belgian Institute, Vision on Technology (VITO) which specializes in remote sensing, we identified the best alternative NVDI source to be from the Moderate Resolution Imaging Spectroradiometer (MODIS) which flies onboard the satellites Aqua and Terra of the National Aeronautic and Space Administration (NASA).                                                   2 NDVI is derived from data collected by National Oceanic and Atmospheric Administration (NOAA) satellites, and processed by the Global Inventory Monitoring and Modeling Studies group (GIMMS) at the National Aeronautical and Space Administration (NASA).   MaikonaNorth HorrCentral and GadamojiLaisamisLoiyangalaniKARGISHURAMAIKONABUBISATURBIILLERETGALASSABARETKOYADARADENORTH HORRDUKANAEL GADEKORRKURUGUMBALESALAISAMISEL-HADIFUROLEKALACHAHAFAREGASHURRI HILLSLOIYANGALANIKURUNGULONTOLIOARAPALLOGOLOGOQILTAMT. KULALMOITEGUDAS/SORIADIKARAREIRIRNGURUNITLARACHIKAMBOYESOUTH HORR(MARSA)LONYORIPICHAUSONGAMERILLEILLAUT(MARSABIT)HULAHULAMAJENGO(MARSABIT)OGUCHOOLTUROTJALDESAKITURUNIDIRIB GOMBOJIRIMESAGANTE Given the policy document agreed by the insuring parties, it was required that we stick to the contractually agreed response function but invoke a clause in the contract that allows for the use of appropriately calibrated as an alternative data source.  We use the MODIS NDVI 16-day composite at a 250m resolution.  In what follows we show how the data were calculated to arrive at the predicted mortality index.     Figure 2. NDVI in Marsabit in 1st dekad of January 2010  3. ZNDVI  In order to take into account the differences in weather impact on vegetation, geographic attributes and resources (soil, vegetation type and topography), we use standardized NDVI, zndvi  for any pixel i of 16-day d in year t :      ( )( )idtdidtdidtidtndvindviEndvizndviσ−=      where idtndvi  is the image of NDVI for pixel i for dekad d of year t, ( )idtd ndviE  is the long-term mean of NDVI values for 16-day d of pixel i taken over 2000-2011 and ( )idtd ndviσ  is the long-term standard deviation of NDVI values for 16-day d of pixel i taken over 2000-2011.  Positive (negative) idtzndvi  represents relatively better (worse) vegetation condition LegendNDVI<VALUE>0 - 0.10.1 - 0.20.2 - 0.30.3 - 0.40.4 - 0.50.5 - 0.60.6 - 0.70.7 - 0.80.8 - 0.90.9 - 1relative to the long-term mean driven by climate.  Figure 3 shows ZNDVI in Marsabit in the 1st dekad of January 2010.  Figure 2 shows that most of Marsabit was very dry in the 1st decade of January but Figure 3 reveals that, at least in the Northern part of Marsabit, it was greener compared to the same dekad in previous years.  Figure 4 shows time series of ZNDVI in North Horr from 2000 to 2010.    Point to Note:  When we needed to announce the indexes for 2010 LRLD contract in early October 2010, the NDVI data for the last 16-day period (14 – 29 September 2010) was not available.  We extrapolated the ZNDVI for the last 16-day period based on the ZNDVI values in the previous 12 months (see Appendix for the detail).       Figure 3. ZNDVI in Marsabit in 1st dekad of January 2010   Zndvi<VALUE>< -1.75-1.75 - -1.25-1.25 - -0.75-0.75 - -0.25-0.25 - 0.250.25 - 0.750.75 - 1.251.25 - 1.75> 1.75Figure 4.  ZNDVI in North Horr from 2000 to 2009   4. Czndvi      To reasonably capture the cumulative impact of climate, we introduce the cumulative path of zndvi (e.g., Czndvi ) into the model. After investigating various cumulative variables with different periods and different ways of cumulating, we identify the following cumulative NDVI variables for inclusion.  Figure 5 shows time flow of insurance coverage periods and NDVI summation periods for the various variables.  Table 1 shows dates and months we assign for each of 16-days.  An annual period is divided into 2 seasons: Long rain long dry (LRLD) season from March to September and short rain short dry (SRSD) season from October to February.  For LRLD insurance coverage, we capture NDVI in the previous SRSD and across the duration of the coverage LRLD.  Similarly, for SRSD insurance coverage, we capture NDVI in the previous LRLD and the SRSD.  Based on these insurance coverage periods and NDVI reading periods, we construct the following 4 types of cumulative ZNDVI variables:  Figure 5. Temporal structure of IBLI Contract  (Insurance coverage periods and NDVI reading periods)  Table 1. Date and month for 16-days 16-day date month 1 1-16 Jan  1 Oct      Nov      Dec       Jan     Feb       Mar       Apr     May     Jun       Jul       Aug      SepLRLD seasonAccumulation process of zndvi∑−==MarOctzndvipreCzndvi,1,1 1_ττ ∑−==SeptOctzndviposCzndvi,3,1 1_ττ∑==SeptMarzndviMinCNzndvi,3,1)0,(ττ∑==SeptMarzndviMaxCPzndvi,3,1)0,(ττMar       Apr      May     Jun       Jul       Aug      Sep     Oct      Nov      Dec      Jan      FebAccumulation process of zndviSRSD season∑−==OctMarzndvipreCzndvi,1,1 1_ττ ∑−==FebMarzndviposCzndvi,3,1 1_ττ∑==FebOctzndviMinCNzndvi,3,1)0,(ττ∑==FebOctzndviMaxCPzndvi,3,1)0,(ττLRLD modelSRSD model 2 17 Jan - 1 Feb  1 3 2-17 Feb  2 4 18 Feb - 5 Mar  2 5 6-21 Mar  3 6 22 Mar - 6 Apr  3 7 7-22 Apr  4 8 23 Apr - 8 May  4 9 9-24 May  5 10 25 May - 9 Jun  5 11 10-25 Jun  6 12 26 Jun - 11 Jul  7 13 12-27 Jul  7 14 28 Jul - 12 Aug  8 15 13-28 Aug  8 16 29 Aug - 13 Sep  9 17 14-29 Sep  9 18 30 Sep - 15 Oct  10 19 16-31 Oct  10 20 1-16 Nov  11 21 17 Nov - 2 Dec  11 22 3-18 Dec  12 23 19-31 Dec  12   1. Czndvi_pos = cumulative ZNDVI represents total cumulative effect of deviations of vegetation condition from normal that are accumulated since the previous rain season to the end of coverage season o ∑∈=sposTddss zndviposCzndvi _ where sposT   = October – September (March – February) if s = LRLD (SRSD).  2. Czndvi_pre = cumulative ZNDVI represents cumulative pre-condition of deviations of vegetation condition from normal accumulated since the previous rain season to the beginning of the coverage season. o ∑∈=spreTddss zndvipreCzndvi _ where spreT  = October – March (March – October) if s = LRLD (SRSD). 3. CNzndvi = cumulative of the negative ZNDVI represents cumulative effect of below normal vegetation condition that during the coverage season. o  ∑∈=sTddss zndviMinCNzndvi )0,(  wheresT  = March – September (October – February) if s = LRLD (SRSD).)  4. CPzndvi = cumulative of the positive ZNDVI represents cumulative effect of above normal vegetation condition during the coverage season.  o ∑∈=sTddss zndviMaxCPzndvi )0,(  wheresT  = March – September (October – February) if s = LRLD (SRSD).   Point to note: The four cumulative standardized NDVI variables above are multiplied by particular values (Table 2) so that magnitudes of the MODIS-based variables would be equivalent to those based on AVHRR NDVI variables available every 10 day.  This is done as the response function was calibrated with AVHRR data.      Table 2. Multiplier for cumulative ZNDVI varialbes insured season variable beginning month ending month # of dekads # of 16-day periods multiplier LRLD Czndvi_pos Oct Sep 36 23 1.57 Czndvi_pre Oct Mar 13 11 1.18 CNzndvi Mar Sep 21 13 1.62 CPzndvi Mar Sep 21 13 1.62 SRSD Czndvi_pos Mar Feb 36 23 1.57 Czndvi_pre Mar Oct 16 14 1.14 CNzndvi Oct Feb 15 10 1.50 CPzndvi Oct Feb 15 10 1.50  Figure 6 shows Czndvi_pre and Czndvi_pos for Oct-Feb (SRSD) insurance period from 2000 to 2009.  As figure shows that 1) we start counting Czndvi in the beginning of March, 2) Czndvi_pre is determined in the end of 1st dekad of October, and 3) Czndiv_pos is determined in the end of February.   Figure 6. Czndvi_pre and Czndvi_pos for Oct-Feb (SRSD)  insurance period from 2000 to 2009  Short rain - Short dry Contract Window (March - February)North Horr - Historical Cumulative ZNDVI (2000-2009) -30-20-1001020301 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Dekad Number2000200120022003200420052006200720082009Czndvi_pre Czndvi_posMar            Apr              May             Jun             Jul               Aug             Sep              Oct          Nov              Dec             Jan             FebMar 6Mar 16Mar 26Apr 6Apr 16Apr 26May 6May 16May 26Jun 6Jun 16Jun 26Jul 6Jul 16Jul 26Aug 6Aug 16Aug 26Sep 6Sep 16Sep 26Oct 6Oct 16Oct 26Nov 6Nov16Nov 26Dec 6Dec 16Dec 26Jan 6Jan 16Jan 26Feb 6Feb 16Feb 26Mar 6Mar 16Mar 26Apr 6Apr 16Apr 26May 6May 16May 26Jun 6Jun 16Jun 26Jul 6Jul 16Jul 26Aug 6Aug 16Aug 26Sep 6Sep 16Sep 26Oct 6Oct 16Oct 26Nov 6Nov16Nov 26Dec 6Dec 16Dec 26Jan 6Jan 16Jan 26Feb 6Feb 16Feb 26Mar 6Mar 16Mar 26Apr 6Apr 16Apr 26May 6May 16May 26Jun 6Jun 16Jun 26Jul 6Jul 16Jul 26Aug 6Aug 16Aug 26Sep 6Sep 16Sep 26Oct 6Oct 16Oct 26Nov 6Nov16Nov 26Dec 6Dec 16Dec 26Jan 6Jan 16Jan 26Feb 6Feb 16Feb 26 5. Predicted Livestock Mortality Index In order to capture the difference in area-averaged mortality responses to climate (strictly speaking, to climate-driven vegetation condition) between moderate and severe climate outcome, we use the following regime switching model in estimating the relationship between Czndvi variables and livestock mortality:    ( ) lslsls ndviXMM 1111 )( ε+=            if 0_ ≥lsposCzndvi     (good-climate regime)   ( ) lslsls ndviXMM 2222 )( ε+=          if 0_ <lsposCzndvi      (bad-climate regime) where the cumulative zndvi  since last rain until the end of the season ( lsposCzndvi _ ) serves as an indicator of seasonal climate outcome to determine regime into which each season belong: either a good-climate regime or a bad one.  The estimation results which derive the predicted livestock mortality index from NDVI are as follows:     Upper Marsabit  o Predicted livestock mortality index for long rain – long dry coverage (M_LRLD):   M_LRLD = 0.0024 × Czndvi_pos if Czndvi_pos >= 0,   M_LRLD = (-0.0187 × Czndvi_pre) + (0.0019 × CNzndvi) + (-0.0064 × CPzndvi) if Czndvi_pos < 0,  o Predicted livestock mortality index for short rain – short dry coverage (M_SRSD):  M_SRSD = 0.0024 × Czndvi_pos if Czndvi_pos >= 0,   M_SRSD = (-0.0187 × Czndvi_pre) + (0.0019 × CNzndvi) + (-0.0064 × CPzndvi) + 0.0354 if Czndvi_pos < 0  Lower Marsabit o Predicted livestock mortality index for long rain – long dry coverage (M_LRLD):  M_LRLD =  (-0.0003 × Czndvi_pre) + (0.0087 × CNzndvi) + (0.0014 × CPzndvi) if Czndvi_pos >= 0  M_LRLD = (-0.0093 × Czndvi_pre) + (0.0117 × CNzndvi) + (-0.0111 × CPzndvi) if Czndvi_pos < 0  o Predicted livestock mortality index for short rain – short dry coverage (M_SRSD):  M_SRSD =  (-0.0003 × Czndvi_pre) + (0.0087 × CNzndvi) + (0.0014 × CPzndvi) + 0.0147 if Czndvi_pos >= 0  M_SRSD = (-0.0093 × Czndvi_pre) + (0.0117 × CNzndvi) + (-0.0111 × CPzndvi) + 0.0446 if Czndvi_pos < 0         Figure 7 shows the time series of predicted livestock mortality index for Oct-Feb (SRSD) insurance period from 2000 to 2009 in North Horr.  Note that the index was determined in the end of short dry season, the most right in the figure, and predicted mortality before the end of short dry season gives us only forecast on the index based on available NDVI data at that point of time.       Figure 7. Forecast of predicted livestock mortality index  for Oct-Feb (SRSD) insurance period  from 2000 to 2009 in North Horr  6. Update on NDVI and Predicted Livestock Mortality Index  See “Index Update and Archive” page on http://www.ilri.org/ibli/  Reference  Chantarat, S., A. G. Mude, C. B. Barrett, and M. R. Carter (2009) “DESIGNING INDEX BASED LIVESTOCK INSURANCE FOR MANAGING ASSET RISK IN NORTHERN KENYA” Working Paper, Cornell University, July. Available at “Papers” page on http://www.ilri.org/ibli/      Short rain - Short dry Contract Window (March - February)North Horr - Predicted Mortality Index (2000-2009) 0%5%10%15%20%25%30%35%40%45%50%1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Dekad Number2000200120022003200420052006200720082009APPENDIX:  Extrapolate ZNDVI for the last 16-day  When we needed to announce the indexes for 2010 LRLD contract in early October 2010, the NDVI data for the last 16-day period (14 – 29 September 2010) was not available.  We extrapolated the ZNDVI for the last 16-day period based on the ZNDVI values in the previous 12 months.  This appendix explains how we extrapolate the ZNDVI.   Denote the ZNDVI for index area i for 16-day d  by ZNDVIid. We regressed ZNDVIid on the ZNDVI in the previous 12 months (22 16-day time period) using ZNDVI data for the 5 index areas from 2000 to 2010.  Table A1 shows the regression results.  We extrapolated the NDVI data for the last 16-day period based on the ZNDVI values in the previous 12 months and estimated regression coefficients.   Table A1. Regression results: ZNDVI in the last 16-day for 2010 LRLD variable coefficient estimate s.e. t-value p-value intercept  -0.0188 0.0634 -0.30 0.77 ZNDVIi,d-22 0.1000 0.1763 0.57 0.58 ZNDVIi,d-21 -0.1379 0.2939 -0.47 0.65 ZNDVIi,d-20 0.2153 0.1149 1.87 0.08 ZNDVIi,d-19 -0.3085 0.2759 -1.12 0.28 ZNDVIi,d-18 0.1791 0.2154 0.83 0.42 ZNDVIi,d-17 0.0796 0.4211 0.19 0.85 ZNDVIi,d-16 0.0396 0.3181 0.12 0.90 ZNDVIi,d-15 -0.1383 0.3681 -0.38 0.71 ZNDVIi,d-14 0.1889 0.4319 0.44 0.67 ZNDVIi,d-13 -0.1473 0.4109 -0.36 0.72 ZNDVIi,d-12 -0.0586 0.2747 -0.21 0.83 ZNDVIi,d-11 0.0727 0.1618 0.45 0.66 ZNDVIi,d-10 -0.1407 0.1227 -1.15 0.27 ZNDVIi,d-9 0.1664 0.2126 0.78 0.44 ZNDVIi,d-8 -0.2175 0.4279 -0.51 0.62 ZNDVIi,d-7 -0.3760 0.4430 -0.85 0.41 ZNDVIi,d-6 0.1966 0.2083 0.94 0.36 ZNDVIi,d-5 0.2609 0.3428 0.76 0.46 ZNDVIi,d-4 0.2709 0.3275 0.83 0.42 ZNDVIi,d-3 -0.0790 0.2638 -0.30 0.77 ZNDVIi,d-2 0.1996 0.5395 0.37 0.72 ZNDVIi,d-1 0.5337 0.3601 1.48 0.16      

https://cgspace.cgiar.org/bitstream/10568/3408/1/DerivePredicted.pdf

Derive predicted livestock mortality index

Abstract

Similar works

Full text

Available Versions

CGSpace (CGIAR)

CGSpace (CGIAR)