{PowerSDI} calculates the Standardized Precipitation (SPI; McKee, Doesken, and Kleist (1993)) and
Standardized Precipitation-Evapotranspiration (SPEI; Sergio M. Vicente-Serrano, Beguerı́a, and López-Moreno
(2010)) indices using gridded-data from the NASA-POWER project.
The package includes functions (ScientSDI(),
Reference(), Accuracy() and
PlotData()), which evaluate how well the drought indices
meet their conceptual assumptions. The OperatSDI() function
allows users to download NASA-POWER data for specific monitoring
periods. The package adopts a quasi-weekly basic time scale
(quart.month), allowing for four index calculations per
month: days 1 to 7, days 8 to 14, days 15 to 21, and days 22 to 28, 29,
30, or 31 depending on the month. For instance, if the time scale is set
to 4 (TS = 4), it corresponds to a moving window with a
1-month length that is calculated four times each month. If
TS = 48, the time scale corresponds to a moving window with
a 12-month length that is calculated four times each month. {PowerSDI}
uses functions from the {nasapower} (A. Sparks
2018; A. H. Sparks et al. 2023) and {Lmom} (Hosking 2023) packages.
Load the library in your R session.
The PlotData() function allows a visual inspection of
the indices’ inputs (precipitation and potential evapotranspiration)
obtained from the NASA-POWER project. These inputs (in millimetres) are
show at the 1-quart.month time scale.
PlotData(
  lon = -47.3,
  lat = -22.65,
  start.date = "1991-01-01",
  end.date = "2022-12-31"
)
#> Just a sec. Downloading NASA POWER data and calculating the other parameters.plot of chunk PlotData
The first step of the SPI and SPEI algorithms is to calculate the
cumulative probabilities of their input variables (Guttman 1999). The ScientSDI()
function estimates the parameters of the gamma, generalized extreme
value (GEV), or generalized logistic distributions (GLO) through the
L-moments method. This function also allows users to replace suspicious
values from the data sample.
The plots generated by the PlotData() function for
Campinas revealed one suspicious rain value larger than 250 mm. Since
this suspicious record represents less than 1% of the data sample, we
replaced it with (RainUplim = 250) before calculating the
parameters of the gamma and GEV distributions. The PE data showed no
suspicious values.
Campinas <- ScientSDI(
  lon = -47.3,
  lat = -22.65,
  start.date = "1991-01-01",
  end.date = "2022-12-31",
  distr = "GEV",
  TS = 4,
  Good = "no",
  RainUplim = 250,
  RainLowlim = NULL,
  PEUplim = NULL,
  PELowlim = NULL
)
#> Removed row(s) above limit: 420 for rain
#> The calculations started on: 1991-01-01Check the SDI values.
head(Campinas$SDI)
#>   Year Month quart.month   Rain  PE.Harg    PE.PM  PPE.Harg    PPE.PM        SPI
#> 1 1991     1           4 244.61 170.7373 146.4035  73.87270  98.20646 0.09109635
#> 2 1991     2           5 314.52 162.4491 135.7954 152.07087 178.72457 1.03838634
#> 3 1991     2           6 323.98 155.9019 131.5357 168.07813 192.44427 1.33262036
#> 4 1991     2           7 300.04 151.1668 128.4917 148.87323 171.54828 1.01676070
#> 5 1991     2           8 209.40 135.6084 115.1231  73.79158  94.27689 0.47371145
#> 6 1991     3           9 240.75 128.9954 109.1543 111.75463 131.59571 1.08669958
#>    SPEI.Harg    SPEI.PM Categ.SPI Categ.SPEI.Harg Categ.SPEI.PM
#> 1 -0.1936137 -0.1557081    Normal          Normal        Normal
#> 2  0.8203645  0.8938564   mod.wet          Normal        Normal
#> 3  1.3080700  1.4026983   mod.wet         mod.wet       mod.wet
#> 4  0.9191998  0.9590826   mod.wet          Normal        Normal
#> 5  0.4402641  0.5283875    Normal          Normal        Normal
#> 6  1.0332707  1.1195075   mod.wet         mod.wet       mod.wetCheck the DistPar
head(Campinas$DistPar)
#>        lon    lat quart.month alfa.rain beta.rain probzero.rain loc.harg  sc.harg
#> [1,] -47.3 -22.65           1  7.408528  29.87982             0 13.73670 74.65810
#> [2,] -47.3 -22.65           2  8.764616  27.03333             0 34.70564 77.84755
#> [3,] -47.3 -22.65           3  9.446275  24.96878             0 36.18941 71.86870
#> [4,] -47.3 -22.65           4  9.797904  25.09108             0 60.80832 88.85291
#> [5,] -47.3 -22.65           5  7.515294  30.45793             0 50.58665 98.79377
#> [6,] -47.3 -22.65           6  8.519209  25.71193             0 40.44269 87.16465
#>         sh.harg   loc.pm     sc.pm      sh.pm TS
#> [1,] 0.04643763 35.10085  77.23558 0.05326288  4
#> [2,] 0.10306408 54.98155  82.17268 0.12652166  4
#> [3,] 0.05582726 54.32006  75.73398 0.05512823  4
#> [4,] 0.35711219 80.30166  96.80879 0.39667736  4
#> [5,] 0.51834901 69.37979 106.06754 0.58681673  4
#> [6,] 0.42728104 55.63610  91.23542 0.44648066  4A basic assumption related to remote sensing data is that they really
represent the “real-world” conditions. Thus, the Accuracy()
function calculates the following measures of accuracy: the absolute
mean error (AME), root-mean-square-error (RMSE), original (dorig),
modified (dmod), refined (dref) Willmott’s indices of agreement, and
Pearson determination coefficient (R2).
In the example below, data("ObsEst") contains pairs of
observed and estimated potential evapotranspiration (PE) data. The
observed and estimated data were obtained from a weather station in
Campinas and from the NASA-POWER project, respectively. PE was estimated
using the Hargreaves & Samani method (Hargreaves and Samani 1985).
Considering that the parameters of the gamma (SPI) and GEV (SPEI)
distributions have already been estimated by the
ScientSDI() function, we can now use the
OperatSDI() function to calculate these two indices on a
routine basis.
The OperatSDI function enables users to download NASA-POWER data only for the period they intend to monitor.
parms <- Campinas$DistPar # Obtained in Example 2
SDI <- OperatSDI(
  lon = -47.3,
  lat = -22.65,
  start.date = "2023-08-01",
  end.date = "2023-08-07",
  parms = Campinas$DistPar,
  TS = 4
)
#> Calculating...
#> Considering the selected `TS`,4, the calculations started on: 2023-06-22
SDI
#>     Lon    Lat Year Month quart.month  Rain       PE       PPE         SPI       SPEI
#> 1 -47.3 -22.65 2023     7          27 15.67 83.24573 -67.57573 -0.17758163 -0.3648784
#> 2 -47.3 -22.65 2023     7          28 16.54 90.45608 -73.91608 -0.09934836 -0.2155000
#> 3 -47.3 -22.65 2023     8          29 16.50 98.82854 -82.32854 -0.23425126 -0.5376825
#>   Categ.SPI Categ.SPEI
#> 1    Normal     Normal
#> 2    Normal     Normal
#> 3    Normal     NormalStandardized indices, both SPI and SPEI are expected to provide
spatially consistent interpretations of their values (Guttman 1999). Therefore, their frequency
distributions are expected to always approach the standard normal
distribution regardless of the region, season, or time scale at which
the indices are calculated (Wu et al. 2006;
Stagge et al. 2015a; Blain, Avila, and Pereira 2017). In this
context, the ScientSDI function calculates two normality-checking
procedures described by Wu et al. (2006)
and Stagge et al. (2015a). Additionally,
the calculation algorithm of the SPI and SPEI relies on fitting a
parametric distribution to their input data. Therefore, the
ScientSDI() function also applies the widely-used
Lilliefors (Lilliefors 1967) and
Anderson-Darling (Anderson and Darling
1954) goodness-of-fit tests to the gamma and GEV/GLO
distributions. The function ScientSDI() allows users to
select significance levels ranging from 5 to 10% to run these tests.
Additionally, the SPEI algorithm often uses the generalized extreme
value (GEV) or the generalized logistic (GLO) [Sergio M. Vicente-Serrano, Beguerı́a, and López-Moreno
(2010); Begueria2013; Stagge et al.
(2015a); Stagge et al. (2015b);
S. M. Vicente-Serrano and Beguerı́a (2015);
Blain, Avila, and Pereira (2017)]. A
review of these studies suggests that the performance of these two
distributions for calculating the SPEI tends to be similar to each other
over most of the range of the index possible values (e.g. -2.0:2:0).
However, these studies also found significant differences between the
two probability functions in the lower and upper tails (S. M. Vicente-Serrano and Beguerı́a 2015). In
this context, the ScientSDI() function also allows the
users to choose between these two models when calculating the SPEI.
Campinas.GEV <- ScientSDI(
  lon = -47.3,
  lat = -22.65,
  start.date = "1991-01-01",
  end.date = "2022-12-31",
  distr = "GEV",
  TS = 4,
  Good = "yes",
  sig.level = 0.95,
  RainUplim = 250,
  RainLowlim = NULL,
  PEUplim = NULL,
  PELowlim = NULL
)
#> Removed row(s) above limit: 420 for rain
#> The calculations started on: 1991-01-01Check the goodness of fit.
head(Campinas.GEV$GoodFit)
#>       Lili.Rain      Crit Lili.PPEHarg      Crit Lili.PPEPM      Crit   AD.Rain
#> [1,] 0.11611448 0.1396603   0.09643114 0.1222336 0.10632197 0.1236653 0.6390502
#> [2,] 0.11600471 0.1428267   0.09792190 0.1253470 0.08309344 0.1267864 0.9182668
#> [3,] 0.13690470 0.1413462   0.13726836 0.1223576 0.13620839 0.1265062 0.8535305
#> [4,] 0.12338364 0.1381886   0.12333484 0.1208748 0.11852563 0.1225573 0.7133716
#> [5,] 0.05656565 0.1435980   0.06200571 0.1226508 0.05552784 0.1203243 0.1413624
#> [6,] 0.07813975 0.1403786   0.08737362 0.1228580 0.09892327 0.1225442 0.6182675
#>           Crit AD.PPEHarg      Crit  AD.PPEPM      Crit
#> [1,] 0.7332467  0.3436237 0.5310983 0.3620798 0.5272992
#> [2,] 0.7060077  0.3130080 0.5854438 0.2911684 0.6386024
#> [3,] 0.7261569  0.5908702 0.5463382 0.6880857 0.5640758
#> [4,] 0.7292376  0.6114124 0.5115284 0.6220234 0.5193580
#> [5,] 0.7369261  0.1526510 0.5074809 0.1144797 0.5235433
#> [6,] 0.7463400  0.2623157 0.5169554 0.3154090 0.5154911Check the normality.
head(Campinas.GEV$Normality)
#>      SPI.Shap            SPI.Shap.p           SPI.AbsMed          
#> [1,] "0.967900296734503" "0.463209059642815"  "0.0997964641569041"
#> [2,] "0.96619340372341"  "0.420858893940406"  "0.0104781137427224"
#> [3,] "0.975582768775712" "0.682405906920205"  "0.129821941048217" 
#> [4,] "0.953414578207946" "0.180061525951205"  "0.168690442662682" 
#> [5,] "0.930008418348121" "0.0391836955173206" "0.291796230478462" 
#> [6,] "0.940736018465501" "0.0785562689884901" "0.198234408496805" 
#>      SPEI.Harg.Shap      SPEI.Harg.Shap.p    SPEI.Harg.AbsMed      
#> [1,] "0.968381434480606" "0.475655103439624" "0.146211508037505"   
#> [2,] "0.965983791350213" "0.415857065519545" "0.0430601773978751"  
#> [3,] "0.977751926965489" "0.747676355214095" "0.146518713888501"   
#> [4,] "0.978980071731148" "0.76943094784405"  "0.000945228380311781"
#> [5,] "0.966177284178725" "0.401102999039477" "0.116531689396188"   
#> [6,] "0.948926963831835" "0.134350899702926" "0.0873165947811334"  
#>      SPEI.PM.Shap        SPEI.PM.Shap.p      SPEI.PM.AbsMed       SPI.testI 
#> [1,] "0.968798285250651" "0.486612320910051" "0.165875549466575"  "Normal"  
#> [2,] "0.975597247176717" "0.682843863812409" "0.109628810903115"  "Normal"  
#> [3,] "0.984353877822483" "0.918729743222738" "0.122398459123283"  "Normal"  
#> [4,] "0.975156717722638" "0.651747489859029" "0.0378055330733986" "Normal"  
#> [5,] "0.967804350100931" "0.441114432321209" "0.106759663113951"  "NoNormal"
#> [6,] "0.944436532965484" "0.100097027435938" "0.116250636028372"  "NoNormal"
#>      SPEI.Harg.testI SPEI.PM.testI SPI.testII SPEI.Harg.testII SPEI.PM.testII
#> [1,] "Normal"        "Normal"      "Normal"   "Normal"         "Normal"      
#> [2,] "Normal"        "Normal"      "Normal"   "Normal"         "Normal"      
#> [3,] "Normal"        "Normal"      "Normal"   "Normal"         "Normal"      
#> [4,] "Normal"        "Normal"      "Normal"   "Normal"         "Normal"      
#> [5,] "Normal"        "Normal"      "NoNormal" "Normal"         "Normal"      
#> [6,] "Normal"        "Normal"      "Normal"   "Normal"         "Normal"Campinas.GLO <- ScientSDI(
  lon = -47.3,
  lat = -22.65,
  start.date = "1991-01-01",
  end.date = "2022-12-31",
  distr = "GLO",
  TS = 4,
  Good = "yes",
  sig.level = 0.95,
  RainUplim = 250,
  RainLowlim = NULL,
  PEUplim = NULL,
  PELowlim = NULL
)
#> Removed row(s) above limit: 420 for rain
#> The calculations started on: 1991-01-01Check the goodness of fit.
head(Campinas.GLO$GoodFit)
#>       Lili.Rain      Crit Lili.PPEHarg      Crit Lili.PPEPM      Crit   AD.Rain
#> [1,] 0.11611448 0.1408241   0.07793223 0.1267743 0.08361417 0.1294131 0.6390502
#> [2,] 0.11600471 0.1438986   0.07754312 0.1248404 0.07863811 0.1290235 0.9182668
#> [3,] 0.13690470 0.1394402   0.11096348 0.1283290 0.10719062 0.1275217 0.8535305
#> [4,] 0.12338364 0.1390644   0.10560516 0.1236858 0.10132682 0.1254306 0.7133716
#> [5,] 0.05656565 0.1378510   0.05057530 0.1234080 0.04670884 0.1240447 0.1413624
#> [6,] 0.07813975 0.1377996   0.11117785 0.1267045 0.12181073 0.1251562 0.6182675
#>           Crit AD.PPEHarg      Crit   AD.PPEPM      Crit
#> [1,] 0.7021159  0.2188857 0.5549677 0.21990399 0.5609734
#> [2,] 0.7345871  0.2930398 0.5376209 0.27915703 0.5696080
#> [3,] 0.7112916  0.4200223 0.5585982 0.51359779 0.5502796
#> [4,] 0.7054471  0.5535407 0.5338313 0.57487863 0.5582377
#> [5,] 0.7249042  0.1123251 0.5474743 0.09516567 0.5540126
#> [6,] 0.7072738  0.4195567 0.5615291 0.50640990 0.5446173Check the normality.
head(Campinas.GLO$GoodFit)
#>       Lili.Rain      Crit Lili.PPEHarg      Crit Lili.PPEPM      Crit   AD.Rain
#> [1,] 0.11611448 0.1408241   0.07793223 0.1267743 0.08361417 0.1294131 0.6390502
#> [2,] 0.11600471 0.1438986   0.07754312 0.1248404 0.07863811 0.1290235 0.9182668
#> [3,] 0.13690470 0.1394402   0.11096348 0.1283290 0.10719062 0.1275217 0.8535305
#> [4,] 0.12338364 0.1390644   0.10560516 0.1236858 0.10132682 0.1254306 0.7133716
#> [5,] 0.05656565 0.1378510   0.05057530 0.1234080 0.04670884 0.1240447 0.1413624
#> [6,] 0.07813975 0.1377996   0.11117785 0.1267045 0.12181073 0.1251562 0.6182675
#>           Crit AD.PPEHarg      Crit   AD.PPEPM      Crit
#> [1,] 0.7021159  0.2188857 0.5549677 0.21990399 0.5609734
#> [2,] 0.7345871  0.2930398 0.5376209 0.27915703 0.5696080
#> [3,] 0.7112916  0.4200223 0.5585982 0.51359779 0.5502796
#> [4,] 0.7054471  0.5535407 0.5338313 0.57487863 0.5582377
#> [5,] 0.7249042  0.1123251 0.5474743 0.09516567 0.5540126
#> [6,] 0.7072738  0.4195567 0.5615291 0.50640990 0.5446173The Accuracy() function may also provide confidence
intervals (CI) for AME, RMSE, dorig, dmod and dref. As emphasized by
Willmott et al. (1985), the CI specifies a
range of values within which these statistics are expected to vary by
chance. Consequently, users can interpret the magnitude of the CI as an
indicator of the reliability of the estimated values for the comparison
metrics Willmott et al. (1985). The
function allows users to select between 90 and 95% CIs.
data("ObsEst")
Compare_PE_Cps_withCI <-
  Accuracy(obs_est = ObsEst,
           conf.int = "yes",
           sig.level = 0.95)
#> Just a sec
Compare_PE_Cps_withCI
#>  AMECIinf      AME AMECIsup RMSECIinf     RMSE RMSECIsup dorig_CIinf     dorig
#>  2.467782 2.470223 2.473673  3.140299 3.144231  3.148564   0.9717026 0.9718557
#>  dorigCIsup dmodCIinf      dmod dmodCIsup dref_CIinf     dref dref_CIsup RQuad_CIinf
#>   0.9718942 0.8382366 0.8386579 0.8387874  0.8377858 0.838266   0.838368   0.9194093
#>      RQuad RQuad_CIsup
#>  0.9197235    0.919914