Evaluation of Geospatial Interpolation Techniques for Enhancing Spatiotemporal Rainfall Distribution and Filling Data Gaps in Asir Region, Saudi Arabia
Abstract
:1. Introduction
Interpolation Method | Validation Method | Recommended Method | Ref. |
---|---|---|---|
Thiessen Polygon (TB), Inverse Distance Weighting (IDW), Linear Regression (LG), Kriging with External Drift (KED), Ordinary Kriging (OK) | Root Mean Squared Error (RMSE) | Ordinary Kriging (OK) | [42] |
Inverse Distance Weighting (IDW), Local Polynomial Interpolation (LPI) Global Polynomial Interpolation (GPI) Simple Kriging (SK) Universal Kriging (UK), Ordinary Kriging (OK), Radial Basis Function (RBF) | Mean Error (ME) Root Mean Squared Error (RMSE) | Ordinary Kriging (OK) | [43] |
Natural Neighbor Interpolation (NNI), Ordinary Kriging (OK) Cokriging (CK) | Root Mean Squared Error (RMSE) | Cokriging (CK) | [44] |
Kriging with External Drift (KED), Optimal Interpolation Method (OIM), Thiessen Polygons (TB) | Root Mean Squared Error (RMSE) | Optimal Interpolation Method (OIM) | [45] |
Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Diffusion Interpolation with Barrier (DIB), Kernel Interpolation with Barrier (KIB), Ordinary Kriging (OK), Empirical Bayesian Kriging (EBK) | Leave-One-Out Cross-Validation (LOOCV), Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE) Nash–Sutcliffe Efficiency Coefficient (NSE) | Kernel Interpolation with Barrier (KIB) | [46] |
Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Local Polynomial Interpolation (LPI), Global Polynomial Interpolation (GPI), Simple Kriging (SK), Universal Kriging (UK), Ordinary Kriging (OK), Empirical Bayesian Kriging (EBK), Empirical Bayesian Kriging Regression Prediction (EBKRP) | Mean Error (ME), Root Mean Square Error (RMSE), Pearson R2 (R2), Mean Standardized Error (MSE), Root Mean Square Standardized Error (RMSSE), Average Standard Error (ASE) | Empirical Bayesian Kriging Regression Prediction (EBKRP) | [47] |
Inverse Distance Weighting (IDW), Kriging, ANUDEM, Spline | Mean Absolute Error (MAE), Mean Relative Error (MRE), Root Mean Squared Error (RMSE), Spatial and Temporal Distributions. | Inverse Distance Weighting (IDW) | [48] |
Inverse Distance Weighting, Natural Neighbor (NN), Regularized Spline (RS), Tension Spline (TS), Ordinary Kriging (OK), Universal Kriging (UK) | Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Bias Error (MBE), Coefficient of Determination (R2) | Ordinary Kriging (OK) | [49] |
Inverse Distance Weighting (IDW), Ordinary Kriging (OK), Ordinary Cokriging (OCK), Linear Regression (LR), Simple Kriging with varying Local Means (SKLM), Kriging with an External Drift (KED) | Mean Error (ME), and Root Mean-Square Error (RMSE) | Ordinary Cokriging (OCK) | [50] |
Circular Ordinary Kriging (COK), Spherical Ordinary Kriging (SOK), Exponential Ordinary Kriging (EOK), Gaussian Ordinary Kriging (GOK), Empirical Bayesian Kriging (EBK) | Mean Error (ME), Mean Standardized Error (MSDE), Root Mean Square Standardized Error (RMSSDE) Mean Standard Error (MSE), Root Mean Square Error (RMSE) | Exponential Ordinary Kriging (EOK), Empirical Bayesian Kriging (EBK) | [51] |
- Assessing various spatial interpolation techniques to ascertain the optimal approach for accurate rainfall prediction across diverse arid regions.
- Analyzing the sufficiency of rainfall station distribution and pinpointing optimal sites for installing new rain gauges within the study area.
- Providing an illustrative example elucidating the practical utilization of study outcomes in filling data gaps at any location and time within the study area for end-users.
2. The Study Area
3. Materials and Methods
3.1. Rain Gauges
3.2. Interpolation Techniques
3.2.1. Deterministic Techniques
3.2.2. Geostatistical Techniques
4. Results and Discussion
5. Use Case
6. Summary and Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Spatial Interpolation Equations and Main Characteristics
- (A)
- Deterministic Approaches
- (A.1.)
- Inverse Distance Weighting (IDW)
- : the predicted unknown value at point .
- : the weight value of the sampled point .
- : the value of the sampled point .
- : the distance between the sampled point and the predicted point .
- : the power of decreasing weight with distance.
- (A.2.)
- Global Polynomial Interpolation
- : location value.
- : random error.
- : parameter.
- (A.3.)
- Local Polynomial Interpolation
- (A.4.)
- Radial Basis Function
- modified Bessel function
- (B)
- Geostatistical Approaches
- : an estimate of the variable of interest at the location .
- the measured value of the variable of interest at the location .
- the Kriging weight of .
- : the total number of data locations.
- (B.1.)
- Simple Kriging
- (B.2.)
- Ordinary Kriging
- the mean value of the stationary variable.
- (B.3.)
- Universal Kriging
- : the number of unbiasedness conditions.
- : the Pth basis function.
- (B.4.)
- Cokriging
- (B.5.)
- Empirical Bayesian Kriging
Interpolation Technique | Advantages | Disadvantages |
---|---|---|
Inverse Distance Weighting |
|
|
Global Polynomial Interpolation |
|
|
Local Polynomial Interpolation |
|
|
Radial Basis Function |
|
|
Kriging |
|
|
Cokriging |
|
|
Empirical Bayesian Kriging |
|
|
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Gauge | Long (WGS 84) | Lat (WGS84) | Altitude (m) | Mean Max. Rainfall (mm) | Mean Total Rainfall (mm) | Gauge | Long (WGS 84) | Lat (WGS 84) | Altitude (m) | Mean Max. Rainfall (mm) | Mean Total Rainfall (mm) |
---|---|---|---|---|---|---|---|---|---|---|---|
A004 | 43.10 | 18.17 | 2280 | 31.9 | 97.9 | J141 | 39.92 | 22.50 | 661 | 49.7 | 96.4 |
A005 | 42.48 | 18.20 | 2186 | 57.3 | 282.8 | J204 | 40.20 | 21.35 | 685 | 39.7 | 154.0 |
A006 | 42.60 | 18.25 | 2121 | 40.3 | 238.5 | J205 | 40.22 | 21.35 | 750 | 46.3 | 171.0 |
A007 | 42.15 | 19.10 | 2376 | 61.8 | 344.4 | J214 | 39.98 | 21.98 | 641 | 33.5 | 97.0 |
A103 | 42.78 | 18.10 | 2224 | 39.5 | 237.9 | J219 | 39.43 | 22.20 | 192 | 22.2 | 38.4 |
A104 | 43.37 | 17.93 | 2281 | 32.1 | 127.2 | J220 | 39.82 | 22.37 | 473 | 23.4 | 62.2 |
A105 | 43.18 | 18.23 | 2206 | 23.9 | 70.1 | J221 | 39.35 | 21.92 | 88 | 27.5 | 45.0 |
A106 | 42.48 | 18.27 | 2356 | 38.5 | 253.2 | J239 | 39.68 | 21.97 | 269 | 23.9 | 64.1 |
A107 | 42.57 | 18.60 | 2016 | 31.9 | 109.8 | N001 | 44.23 | 17.55 | 1278 | 19.8 | 44.5 |
A108 | 42.38 | 18.52 | 2516 | 26.4 | 85.0 | N103 | 43.63 | 17.68 | 2191 | 34.2 | 145.9 |
A110 | 42.98 | 18.68 | 1802 | 33.9 | 98.3 | N203 | 43.62 | 17.67 | 2036 | 26.9 | 94.3 |
A112 | 42.57 | 18.37 | 2096 | 36.2 | 112.4 | SA001 | 42.95 | 17.05 | 169 | 36.4 | 203.0 |
A113 | 42.68 | 18.63 | 1840 | 17.5 | 69.3 | SA002 | 42.62 | 17.17 | 32 | 28.2 | 80.2 |
A117 | 42.27 | 18.62 | 2489 | 38.2 | 181.7 | SA003 | 41.88 | 19.00 | 355 | 37.5 | 202.7 |
A118 | 42.37 | 18.25 | 2197 | 56.7 | 333.7 | SA004 | 41.40 | 18.73 | 41 | 27.4 | 61.2 |
A120 | 42.17 | 18.88 | 2308 | 56.0 | 213.9 | SA005 | 41.88 | 19.56 | 2263 | 27.2 | 172.5 |
A121 | 42.75 | 18.03 | 2269 | 44.5 | 292.7 | SA101 | 42.83 | 16.97 | 68 | 41.6 | 173.0 |
A123 | 42.87 | 18.32 | 2039 | 34.3 | 128.9 | SA102 | 42.23 | 17.70 | 51 | 30.1 | 65.2 |
A124 | 42.33 | 18.42 | 2577 | 41.0 | 185.0 | SA104 | 43.08 | 17.04 | 574 | 50.3 | 403.9 |
A126 | 43.22 | 18.53 | 1850 | 12.9 | 26.5 | SA105 | 41.97 | 18.93 | 458 | 48.6 | 364.1 |
A127 | 42.25 | 18.78 | 2531 | 48.3 | 247.3 | SA106 | 42.53 | 17.37 | 73 | 37.2 | 137.5 |
A128 | 42.70 | 18.47 | 1927 | 16.5 | 60.2 | SA107 | 42.78 | 17.12 | 78 | 44.6 | 170.0 |
A130 | 42.32 | 18.33 | 2470 | 36.1 | 216.5 | SA108 | 41.92 | 18.33 | 533 | 41.8 | 255.8 |
A201 | 42.52 | 18.42 | 2083 | 25.9 | 103.0 | SA110 | 43.13 | 17.27 | 1210 | 47.1 | 401.0 |
A206 | 42.25 | 18.68 | 2603 | 39.1 | 206.6 | SA111 | 43.12 | 17.05 | 574 | 54.5 | 444.1 |
A213 | 42.83 | 18.17 | 2114 | 30.4 | 132.0 | SA113 | 42.03 | 18.53 | 455 | 41.3 | 298.1 |
B001 | 41.29 | 20.18 | 1932 | 58.9 | 294.0 | SA115 | 41.67 | 18.00 | 0 | 28.1 | 54.6 |
B004 | 42.60 | 20.02 | 1155 | 21.3 | 71.8 | SA116 | 42.20 | 18.25 | 1421 | 49.0 | 321.7 |
B005 | 42.53 | 19.87 | 1202 | 18.6 | 73.6 | SA120 | 41.83 | 19.43 | 611 | 46.2 | 243.5 |
B006 | 43.52 | 19.53 | 1090 | 21.8 | 48.9 | SA122 | 41.83 | 19.12 | 377 | 31.1 | 208.6 |
B007 | 41.57 | 19.87 | 2047 | 52.6 | 269.3 | SA125 | 42.45 | 17.13 | 7 | 25.8 | 72.5 |
B008 | 42.67 | 20.08 | 1139 | 24.3 | 80.1 | SA126 | 42.88 | 17.45 | 559 | 45.9 | 502.3 |
B009 | 41.90 | 19.53 | 2279 | 46.0 | 272.6 | SA129 | 42.90 | 17.17 | 163 | 49.9 | 313.7 |
B101 | 41.58 | 19.90 | 2040 | 50.8 | 224.9 | SA132 | 42.78 | 17.02 | 61 | 29.5 | 127.0 |
B103 | 41.65 | 20.25 | 1571 | 20.0 | 51.5 | SA135 | 43.23 | 16.80 | 287 | 43.7 | 330.6 |
B110 | 42.88 | 18.80 | 1742 | 22.4 | 73.2 | SA136 | 43.13 | 16.68 | 159 | 45.6 | 251.7 |
B111 | 42.85 | 21.25 | 922 | 18.4 | 48.8 | SA137 | 42.95 | 16.60 | 61 | 29.5 | 116.3 |
B114 | 42.23 | 20.02 | 1286 | 25.5 | 98.2 | SA138 | 42.02 | 18.63 | 393 | 39.7 | 267.1 |
B208 | 42.73 | 19.02 | 1717 | 20.3 | 69.6 | SA139 | 42.03 | 19.05 | 900 | 26.2 | 293.3 |
B216 | 41.98 | 19.47 | 2239 | 42.9 | 234.8 | SA140 | 43.03 | 17.32 | 688 | 49.7 | 448.6 |
B217 | 41.93 | 19.75 | 1756 | 43.0 | 170.4 | SA142 | 41.58 | 18.77 | 104 | 32.3 | 101.9 |
B219 | 42.80 | 19.33 | 1475 | 18.4 | 53.1 | SA143 | 43.13 | 16.90 | 259 | 46.3 | 420.7 |
B220 | 42.04 | 19.20 | 1571 | 36.0 | 142.6 | SA144 | 42.25 | 18.17 | 1013 | 46.9 | 366.6 |
J001 | 41.05 | 19.53 | 53 | 36.8 | 77.3 | SA145 | 42.80 | 17.62 | 699 | 46.0 | 306.8 |
J002 | 39.34 | 22.16 | 72 | 18.3 | 33.3 | SA147 | 41.47 | 19.03 | 115 | 30.9 | 66.3 |
J102 | 39.70 | 21.43 | 355 | 27.8 | 50.3 | SA148 | 42.53 | 16.92 | 0 | 35.5 | 79.0 |
J106 | 39.33 | 22.15 | 66 | 18.8 | 35.8 | SA204 | 42.60 | 17.57 | 188 | 43.3 | 160.2 |
J107 | 40.45 | 20.32 | 95 | 34.1 | 63.6 | TA002 | 40.50 | 21.30 | 1590 | 33.0 | 148.2 |
J108 | 40.28 | 20.15 | 7 | 32.8 | 59.8 | TA004 | 40.45 | 21.40 | 1553 | 28.6 | 119.4 |
J111 | 38.83 | 23.10 | 12 | 17.4 | 33.7 | TA005 | 41.67 | 21.18 | 1148 | 14.0 | 49.4 |
J113 | 40.12 | 21.37 | 455 | 47.8 | 146.0 | TA006 | 41.28 | 20.62 | 1389 | 52.6 | 117.9 |
J114 | 39.82 | 21.43 | 298 | 37.9 | 78.6 | TA007 | 41.47 | 19.98 | 2256 | 48.6 | 194.0 |
J116 | 39.63 | 22.58 | 394 | 28.2 | 63.3 | TA104 | 40.80 | 21.32 | 1394 | 31.4 | 97.3 |
J121 | 41.05 | 20.23 | 338 | 40.9 | 162.1 | TA106 | 40.32 | 21.33 | 1888 | 44.8 | 185.5 |
J124 | 41.28 | 19.95 | 586 | 30.0 | 114.4 | TA109 | 40.37 | 21.07 | 2145 | 45.4 | 269.6 |
J126 | 41.43 | 19.77 | 353 | 37.3 | 236.8 | TA125 | 40.42 | 21.26 | 1713 | 29.7 | 51.7 |
J127 | 41.53 | 19.67 | 657 | 52.7 | 184.0 | TA206 | 40.40 | 21.28 | 1675 | 35.7 | 165.8 |
J131 | 41.60 | 19.47 | 474 | 41.9 | 182.6 | TA233 | 40.65 | 21.13 | 1691 | 48.5 | 205.6 |
J134 | 39.20 | 21.50 | 15 | 28.7 | 51.4 | TA250 | 40.45 | 21.67 | 1241 | 22.7 | 91.2 |
J137 | 41.33 | 19.97 | 632 | 36.4 | 222.3 | TA251 | 40.37 | 21.37 | 1822 | 30.1 | 120.1 |
J139 | 41.03 | 19.73 | 93 | 38.6 | 63.9 | TA255 | 40.36 | 21.24 | 1730 | 34.1 | 118.5 |
J140 | 39.03 | 22.82 | 10 | 21.1 | 39.4 |
Geostatistical Interpolation Techniques | |
---|---|
Ordinary Kriging—Circular Variogram (KOC) | Ordinary Cokriging—Circular Variogram (CKOC) |
Ordinary Kriging—Spherical Variogram (KOS) | Ordinary Cokriging—Spherical Variogram (CKOS) |
Ordinary Kriging—Exponential Variogram (KOE) | Ordinary Cokriging—Exponential Variogram (CKOE) |
Ordinary Kriging—Gaussian Variogram (KOG) | Ordinary Cokriging—Gaussian Variogram (CKOG) |
Ordinary Kriging—K-Bessel Variogram (KOK) | Ordinary Cokriging—K-Bessel Variogram (CKOK) |
Ordinary Kriging—J-Bessel Variogram (KOJ) | Ordinary Cokriging—J-Bessel Variogram (CKOJ) |
Ordinary Kriging—Stable Variogram (KOT) | Ordinary Cokriging—Stable Variogram (CKOT) |
Simple Kriging—Circular Variogram (KSC) | Simple Cokriging—Circular Variogram (CKSC) |
Simple Kriging—Spherical Variogram (KSS) | Simple Cokriging—Spherical Variogram (CKSS) |
Simple Kriging—Exponential Variogram (KSE) | Simple Cokriging—Exponential Variogram (CKSE) |
Simple Kriging—Gaussian Variogram (KSG) | Simple Cokriging—Gaussian Variogram (CKSG) |
Simple Kriging—K-Bessel Variogram (KSK) | Simple Cokriging—K-Bessel Variogram (CKSK) |
Simple Kriging—J-Bessel Variogram (KSJ) | Simple Cokriging—J-Bessel Variogram (CKSJ) |
Simple Kriging—Stable Variogram (KST) | Simple Cokriging—Stable Variogram (CKST) |
Universal Kriging—Circular Variogram (KUC) | Universal Cokriging—Circular Variogram (CKUC) |
Universal Kriging—Spherical Variogram (KUS) | Universal Cokriging—Spherical Variogram (CKUS) |
Universal Kriging—Exponential Variogram (KUE) | Universal Cokriging—Exponential Variogram (CKUE) |
Universal Kriging—Gaussian Variogram (KUG) | Universal Cokriging—Gaussian Variogram (CKUG) |
Universal Kriging—K-Bessel Variogram (KUK) | Universal Cokriging—K-Bessel Variogram (CKUK) |
Universal Kriging—J-Bessel Variogram (KUJ) | Universal Cokriging—J-Bessel Variogram (CKUJ) |
Universal Kriging—Stable Variogram (KUT) | Universal Cokriging—Stable Variogram (CKUT) |
Empirical Bayesian Kriging (EBK) | |
Deterministic interpolation techniques | |
Global Polynomial Interpolation (GPI) | Inverse Distance Weighting—P = 2 (IDWP2) |
Local Polynomial Interpolation (LPI) | Inverse Distance Weighting—P = 3 (IDWP) |
Radial Basis Function (RBF) | Inverse Distance Weighting—P = 4 (IDWP4) |
Inverse Distance Weighting (P = 1) (IDWP1) | Inverse Distance Weighting—P = 5 (IDWP) |
Year | Total Yearly | Maximum Daily | Year | Total Yearly | Maximum Daily |
---|---|---|---|---|---|
1966 | KOJ | CKOK | 1990 | CKUK | CKOJ |
1967 | KUJ | KUJ | 1991 | CKSJ | KOJ |
1968 | KSJ | CKUC | 1992 | CKOJ | KSG |
1969 | LPI | CKOJ | 1993 | CKUJ | CKSK |
1970 | KSJ | KUJ | 1994 | CKOS | KOJ |
1971 | CKOC | CKOC | 1995 | CKOC | CKUC |
1972 | CKOC | KOJ | 1996 | CKSE | CKOG |
1973 | CKOJ | KOJ | 1997 | CKUT | CKOT |
1974 | KOJ | CKOC | 1998 | CKUK | CKOK |
1975 | CKOJ | CKUJ | 1999 | CKSG | CKOC |
1976 | CKOJ | LPI | 2000 | KSG | KOE |
1977 | CKOG | CKUC | 2001 | KOT | KSJ |
1978 | CKOJ | KUJ | 2002 | CKSC | CKOG |
1979 | CKOT | CKOS | 2003 | KUJ | CKSJ |
1980 | KOJ | CKOJ | 2004 | KOJ | CKOJ |
1981 | CKSG | CKSJ | 2005 | CKSC | GPI |
1982 | CKSG | CKUJ | 2006 | KOG | CKOK |
1983 | CKUC | KOJ | 2007 | KOG | IDWP1 |
1984 | CKOC | CKSK | 2008 | CKSJ | CKSG |
1985 | CKOE | CKOK | 2009 | CKSE | KUJ |
1986 | CKOC | KUJ | 2010 | KSG | CKOC |
1987 | KOJ | CKSK | 2011 | KSJ | KST |
1988 | KUK | CKOC | 2012 | CKOS | CKUJ |
1989 | CKUE | LPI | 2013 | CKOJ | CKOC |
Maximum Rainfall Error (%) | Total Rainfall Error (%) | Error Summation (%) | |
---|---|---|---|
Existing stations | 14.60% | 27.08% | 41.68% |
Existing stations + Proposed stations (I) | 12.71% | 22.34% | 35.05% |
Existing stations + Proposed stations (I) and (II) | 11.65% | 20.95% | 32.61% |
Existing stations + Proposed stations (I), (II), and (III) | 11.51% | 20.79% | 32.31% |
Aridity Level | Aridity Index (AI) |
---|---|
Desert | AI < 0.03 |
Hyper arid | 0.03 < AI < 0.05 |
Arid | 0.05 < AI < 0.20 |
Semi-arid | 0.20 < AI < 0.50 |
Dry | 0.50 < AI < 0.65 |
Sub-humid | 0.65 < AI < 0.75 |
Humid | AI > 0.75 |
Cold | PET ≤ 400 mm |
J124 | B001 | J137 | J126 | TA007 | J127 | B007 | B101 | |
---|---|---|---|---|---|---|---|---|
2008 | 23.0 | 32.0 | missing | 26.78991 | 26.0 | missing | 46.0 | 19.0 |
2009 | 34.0 | 63.0 | missing | 33.0 | 54.5 | missing | 42.5 | 25.0 |
2010 | 60.0 | 56.0 | missing | 41.0 | 168.0 | missing | 54.0 | 45.0 |
2011 | 28.0 | 82.5 | missing | 22.0 | 60.0 | missing | 44.0 | 27.0 |
2012 | 40.0 | missing | missing | 17.0 | 34.5 | missing | 62.0 | 56.0 |
2013 | 26.5 | missing | missing | 28.0 | 24.5 | missing | 54.0 | 40.0 |
2014 | 7.3 | 30.8 | 70.4 | 35.5 | 37.8 | 40.5 | 36.1 | 41.5 |
2015 | 6.5 | 89.0 | 51.3 | 51.5 | missing | 50.8 | 59.0 | missing |
2016 | 32.0 | 69.0 | 50.5 | 50.8 | missing | 50.5 | 26.0 | 52.0 |
2017 | 1.3 | 78.8 | 24.5 | 21.6 | missing | 45.3 | 26.2 | 15.0 |
2018 | 5.0 | 34.4 | 42.5 | 21.5 | missing | 40.5 | 35.8 | 34.5 |
J124 | B001 | J137 | J126 | TA007 | J127 | B007 | B101 | |
---|---|---|---|---|---|---|---|---|
2008 | 23.0 | 32.0 | 27.2 | 26.8 | 26.0 | 28.2 | 46.0 | 19.0 |
2009 | 34.0 | 63.0 | 46.4 | 33.0 | 54.5 | 51.4 | 42.5 | 25.0 |
2010 | 60.0 | 56.0 | 46.4 | 41.0 | 168.0 | 42.6 | 54.0 | 45.0 |
2011 | 28.0 | 82.5 | 30.4 | 22.0 | 60.0 | 22.9 | 44.0 | 27.0 |
2012 | 40.0 | 19.4 | 26.8 | 17.0 | 34.5 | 32.4 | 62.0 | 56.0 |
2013 | 26.5 | 30.0 | 30.9 | 28.0 | 24.5 | 32.5 | 54.0 | 40.0 |
2014 | 7.3 | 30.8 | 70.4 | 35.5 | 37.8 | 40.5 | 36.1 | 41.5 |
2015 | 6.5 | 89.0 | 51.3 | 51.5 | 50.4 | 50.8 | 59.0 | 52.9 |
2016 | 32.0 | 69.0 | 50.5 | 50.8 | 47.2 | 50.5 | 26.0 | 52.0 |
2017 | 16.0 | 78.8 | 24.5 | 21.6 | 24.4 | 45.3 | 26.2 | 15.0 |
2018 | 5.0 | 34.4 | 42.5 | 21.5 | 30.6 | 40.5 | 35.8 | 34.5 |
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Helmi, A.M.; Elgamal, M.; Farouk, M.I.; Abdelhamed, M.S.; Essawy, B.T. Evaluation of Geospatial Interpolation Techniques for Enhancing Spatiotemporal Rainfall Distribution and Filling Data Gaps in Asir Region, Saudi Arabia. Sustainability 2023, 15, 14028. https://doi.org/10.3390/su151814028
Helmi AM, Elgamal M, Farouk MI, Abdelhamed MS, Essawy BT. Evaluation of Geospatial Interpolation Techniques for Enhancing Spatiotemporal Rainfall Distribution and Filling Data Gaps in Asir Region, Saudi Arabia. Sustainability. 2023; 15(18):14028. https://doi.org/10.3390/su151814028
Chicago/Turabian StyleHelmi, Ahmed M., Mohamed Elgamal, Mohamed I. Farouk, Mohamed S. Abdelhamed, and Bakinam T. Essawy. 2023. "Evaluation of Geospatial Interpolation Techniques for Enhancing Spatiotemporal Rainfall Distribution and Filling Data Gaps in Asir Region, Saudi Arabia" Sustainability 15, no. 18: 14028. https://doi.org/10.3390/su151814028