1. Introduction
 To the best of our knowledge, slant link rain fade models have not been classified broadly. In this work, we have prepared a taxonomy of the rain fade models for Earth–space links.
 A brief overview of each of the models selected is presented. In addition, we have provided algorithms of different models.
 Quantitative and qualitative characteristics of different models are organized in tables to review comparative studies.
 We noticed that each model was improved inherently and criticized the prototype by finding the inconveniences, and the specific characteristics are listed.
 Finally, the open research issues are summarized.
2. Background Study
2.1. Rain Attenuation Parameters
2.2. Earth–Space Link Budget
2.3. Rain Attenuation Anomalies: Breakpoint
2.4. Slant Path in Rain Cell
2.4.1. Rain Height
2.4.2. Effective Slant Path
2.5. Rainfall Rate Conversion
2.6. Rain Type
2.7. Rain Cell Size
2.8. Rainfall Rate Missing Data
2.8.1. Temporal Missing: Time Series (TS)
2.8.2. Temporal Missing: Generation by Synthetic Means
2.9. Effective Rainfall Rate
2.10. Raindrop Size Distribution
3. Models to Predict Slant Link Attenuation
 Empirical models: The model depends on experimental data findings rather than mathematically describable input–output relationships.
 Physical models: In the physical model, there exists some physical resemblance between the formulated rain attenuation model and the physical structure of rain.
 Statistical models: This type of model is built on the longterm data of rain attenuation, rainfall rate, and related atmospheric parameter statistical analysis.
 Fade slope models: In the fade slope model, a change in rain attenuation is determined from the fluctuations of measured experimental rain attenuation over time. These results can subsequently be used to forecast the attenuation of rain.
 Learningbased models: The learningbased rain attenuation is new in the domain of knowledge. Longterm rain attenuation and huge datasets of related parameters are used as the input to a learning network (i.e., artificial neural network) to train, and later this trained network (e.g., optimized weights) can be used to predict rain attenuation.
4. Review: Slant Links Rain Fade Models
4.1. Empirical Model
4.1.1. SAM
 (1)
 Calculate specific attenuation:$${\gamma}_{\mathrm{decay}}\left(R\right)=k{R}^{\alpha}\phantom{\rule{4pt}{0ex}}(\mathrm{dB}/\mathrm{km})$$
 (2)
 The rainfall rate varies along with the link, and the rainfall rate can be defined as:$$R\left(l\right)=\left\{\begin{array}{cc}{R}_{p}& {R}_{p}\le 10\phantom{\rule{4pt}{0ex}}\mathrm{mm}/\mathrm{h}\\ {R}_{p}{e}^{{\gamma}_{\mathrm{decay}}ln({R}_{p}/10)lcos\theta}& {R}_{p}\ge 10\phantom{\rule{4pt}{0ex}}\mathrm{mm}/\mathrm{h}\end{array}\right.$$$${L}_{S}=\frac{{H}_{R}{H}_{S}}{sin\theta}$$$${H}_{R}=\left\{\begin{array}{cc}4.8\hfill & \mathrm{if}\phantom{\rule{3.33333pt}{0ex}}\left\phi \right\le {30}^{\circ}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathrm{R}}_{p}\le 10\phantom{\rule{4pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \\ 7.80.1\left\phi \right\hfill & \mathrm{if}\phantom{\rule{3.33333pt}{0ex}}\left\phi \right\ge {30}^{\circ}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathrm{R}}_{p}\ge 10\phantom{\rule{4pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \end{array}\right.$$
 (3)
 Finally the rain attenuation is determined by Equation (19):$$A\left({R}_{0}\right)=\left\{\begin{array}{cc}{R}_{p}^{\alpha}{L}_{S}\hfill & \mathrm{if}\phantom{\rule{3.33333pt}{0ex}}{R}_{p}\le 10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \\ \frac{\left(k{R}_{p}^{\alpha}\right)(1exp\left[\alpha {\gamma}_{\mathrm{decay}}ln\left({R}_{p}/10\right){L}_{S}cos\theta \right])}{\alpha {\gamma}_{\mathrm{decay}}ln\left({R}_{p}/10\right)cos\theta}\hfill & \mathrm{if}\phantom{\rule{3.33333pt}{0ex}}{R}_{p}\ge 10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \end{array}\right.$$
Algorithm 1: SAM Model [32] 
Advantages
Limitations
4.1.2. Singapore Model
Advantages
Limitations
Algorithm 2: Singapore Model [33] 

4.1.3. Garcia Lopez Model
Algorithm 3: Garcia Lopez Model [34] 

Advantages
Limitations
4.1.4. GSST Model
Advantages
Limitations
4.1.5. LU Model
Algorithm 4: GSST Model [66] 
 (1)
 The distribution of rainfall rate projection on the Earth is defined as:$$R(x,p)={R}_{max}\left(p\right){e}^{b\leftx{L}_{G}\right}$$
 (2)
 The attenuation along with the slant link:$$A\left(p\right)=k{\left[R\left(p\right)r\left(p\right)\right]}^{\alpha}{L}_{S}$$
 (3)
 The coefficients ${a}_{i}\phantom{\rule{0.166667em}{0ex}}(i=1,2,\dots ,6)$ are taken using the genetic algorithm (GA) and annealing algorithm; thus, exploiting the rain databank of the ITUR for the slant link:$$r\left(p\right)=3.78(1\frac{0.85{p}^{0.065}}{1+0.12{L}_{S}})R{\left(p\right)}^{0.56+\frac{1.51}{{L}_{S}}}$$
Algorithm 5: LU Model [68] 
//$\phantom{(}$ Assumption: abrupt change more than 1 dB is neglected $\phantom{(}$

Advantages
Limitations
4.1.6. Karasawa Model
Algorithm 6: Karasawa Model [88] 

Advantages
Limitations
4.1.7. Breakpoint Model
 (1)
 Calculate the “percentage of exceedance” at the breakpoint:$${p}_{{R}_{B}}\phantom{\rule{0.277778em}{0ex}}of\phantom{\rule{0.277778em}{0ex}}0.01\%={p}_{{A}_{B}}\phantom{\rule{0.277778em}{0ex}}of\phantom{\rule{0.277778em}{0ex}}0.021\%$$
 (2)
 Compute:$${A}_{p}=\left\{\begin{array}{cc}{A}_{B}{\left(\frac{p0.011}{0.01}\right)}^{{P}_{1}},\hfill & 0.021\le p<1\\ {A}_{B}{\left(\frac{p}{0.021}\right)}^{{P}_{2}},\hfill & p<0.021\end{array}\right.$$$$\begin{array}{c}\hfill {P}_{1}=(0.655+0.033ln(p0.011)\\ \hfill 0.045ln\left({A}_{B}\right)\beta (0.989p)sin\theta )\end{array}$$$$\begin{array}{c}\hfill {P}_{2}=0.5(0.655+0.033ln\left({p}^{2}\right)\\ \hfill 0.045ln\left({A}_{B}\right)\beta (0.989p)sin\theta )\end{array}$$
Algorithm 7: Breakpoint Model [29] 
Advantages
Limitations
4.1.8. Unified Model
Algorithm 8: Unified Model [89] 

Advantages
Limitations
4.1.9. YJ.X. Yeo, Y.H. Lee and J.T. Ong (YLO) Model
Algorithm 9: YLO Model [12] 
Advantages
Limitations
4.2. Statistical Models
4.2.1. Maseng–Bakken (MK) Model
Algorithm 10: MK Model [90] 

Advantages
Limitations
4.2.2. Modified Genetic AlgorithmARIMA (MARIMA) Model
Algorithm 11: MARIMA model [91] 
Advantages
Limitations
4.2.3. ITUR P.618 Model
Algorithm 12: ITUR P.618 Model [45] 
Advantages
Limitations
4.2.4. PEARP Model
Algorithm 13: PEARP model [92] 

Advantages
Limitations
4.2.5. Das Model
Algorithm 14: Das Model [93] 
Advantages
Limitations
4.3. Physical Models
4.3.1. Bryant Model
Algorithm 15: Bryant Model [37] 
Advantages
Limitations
4.3.2. Crane TC
Algorithm 16: Crane TC [94] 
Advantages
Limitations
4.3.3. PhysicalMathematical (PM) Model
Algorithm 17: PM Model [95] 
Advantages
Limitations
4.3.4. SCEXCELL Model
Algorithm 18: SCEXCELL Model [62] 
Advantages
Limitations
4.4. Fade Slope Model
4.4.1. Japan Model
Algorithm 19: Japan Model [96] 
/* Choose proper sampling time to avoid aliasing effect on $X\left(t\right)$ */ 1 Find X_{low} /* Apply Equation (53) */ 2 Find X_{high} /* Apply Equation (54) */ 3 Apply FFT /* Choose number of FFT points for better visualization */ 4 Generate time domain diagram /* To observe the fluctuations */ 
Advantages
Limitations
4.4.2. Das Fade Model
Algorithm 20: Das Fade slope model [133] 
1 Apply LPF and MAF; 2 Find the fade slope; 3 Calculate PDF /* PDF: probability density function */ 4 Extract statistical coefficient (${\sigma}_{\zeta}$) /* ${\sigma}_{\zeta}$: standard deviation of $\zeta $ */ 5 Fit polynomial to fit attenuation with ${\sigma}_{\zeta}$ 6 Use $\zeta $ to calculate rain attenuation for time series data prediction (${A}_{p}$) 7 Return ${A}_{p}$ 
Advantages
Limitations
4.4.3. ITUR P.1623
Algorithm 21: ITUR P.1623 model [98] 
1 Calculate F /*$\phantom{(}$ Equation (59)$\phantom{(}$ */ 2 Calculate ${\sigma}_{\zeta}$ /*$\phantom{(}$ Equation (60)$\phantom{(}$ */ 3 Calculate $P\left(\zeta \rightA)$ /*$\phantom{(}$ Equation (61)$\phantom{(}$ */ Return A 
Advantages
Limitations
4.4.4. Dao Model
Algorithm 22: Dao model [99] 

Advantages
Limitations
4.5. LearningBased Model
4.5.1. Ahuna Model
Advantages
Limitations
5. Comparative Study of Slant Link Rain Fade Models
6. Future Research Scope
6.1. Scaling Improvement
6.2. NonUniformity of Isothermal Heights
6.3. Spatial Rainfall Distribution Along Slant Link
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
2D SST  2Dimentional SST 
ARIMA  Autoregressive integrated moving average 
BBH  Bright band height 
BPNN  Backpropagation neural network 
CCDF  Complementary cumulative distribution function 
CCIR  Comité Consultatif International des Radiocommunications 
CDF  Cumulative distribution function 
DBSG3  Study group 3 databanks 
DSD  Drop size distribution 
ECMWF  European Center for MediumRange Weather Forecasts 
EMPI  Empirical 
ERA15  ECMWF ReAnalysis15 
ESST  Enhanced synthetic storm technique 
EXCELL  EXponential CELL 
FADE  Fade slope 
FFT  Fast Fourier transform 
FSL  Free space path loss 
GA  Genetic algorithm 
GE23  General Electric 23 
GEO  Geostationary 
GRV  Gaussian random variable 
GSST  Global synthetic storm technique 
HYCELL  Hybrid CELL 
IDW  Inverse distance weighting 
INTELSAT  International Telecommunications Satellite Organization 
IoT  Internet of Things 
ITUR  International Telecommunication UnionRadiocommunication sector 
LB  Learningbased 
LEO  LowEarth orbit 
LPF  Lowpass filter 
MAF  Moving average filter 
MARIMA  Modified genetic algorithmARIMA 
MEO  MediumEarth orbit 
MK  Maseng–Bakken 
MultiEXCELL  MultiEXCELL 
NM  Not mentioned 
Probability density function  
PEARP  Prévision d’Ensemble ARPEGE 
PHY  Physical 
PLF  Path length factor 
PM  Physicalmathematical 
POR  Pacific Ocean Region 
PRF  Path reduction factor 
RF  Reduction factor 
RHCP  Righthand circular polarization 
RMS  Root mean square 
RMSE  Root mean square error 
RN  Random number 
RSL  Received signal level 
RV  Random variable 
SAM  Simple rain attenuation model 
SCEXCELL  Stratiform convective exponential CELL model 
SNR  Signaltonoise ratio 
SST  Synthetic storm technique 
STAT  Statistical 
STD  Standard deviation 
TC  Two component 
TS  Time series 
UAV  Unmanned aerial vehicle 
VDK  Van de Kamp 
WINDS  Wideband InterNetworking engineering test and Demonstration Satellite 
Meanings of Used Symbols  
$\Delta {x}_{0}$  A shift along horizontal axis due to the presence of layer B (Figure 2) 
${\Gamma}_{\tau}\left(R\right)$  Rainfall rate conversion factor 
${\gamma}_{decay}$  Decay profile along horizontal axis [Equation (16)] 
$\gamma $  Specific attenuation 
$\Lambda (\cdots )$  Lognormal distribution 
${\lambda}_{0}$  Freespace wavelength (m) $\left({\lambda}_{0}=\frac{0.3}{f\left(GHz\right)}\right)$ 
$\rho $  Rain cell radius 
$\theta $  Elevation angle in degrees of the earth station 
$\phi $  Latitude of the earth station (degrees) 
$\zeta $  Slant path 
${v}_{0.01}$  Vertical adjustment factor (Algorithm 7) 
$a\left(R\right)$  Horizontal length of rain cell 
$a,b$  Coefficient defined in “characteristic length” (Algorithm 6) 
${A}_{B}$  Breakpoint attenuation [Equation (23)] 
${A}_{p}$  Rain attenuation [Equation (13)] 
${A}_{s}$  Slant path attenuation 
$b\left(R\right)$  Slant length of rain cell 
B  Bandwidth (Hz) 
${CF}_{60}$  Rainfall rate conversion factor 
D  Rain cell diameter [Equation (36)] 
${G}_{rx}$  Receive antenna gain 
${G}_{tx}$  Transmit antenna gain 
${H}_{R}^{\prime}$  Top of melting level 
${H}_{R}$  Rain height 
${H}_{S}$  Height above mean sea level of the earth station (km) 
${H}_{0}$  ${0}^{\circ}$ isotherm height 
${I}_{x},{I}_{y}$  Central moments of inertia 
k  Boltzmann constant $=1.38\times {10}^{23}$ J / K 
${L}_{0}$  Characteristic length 
${L}_{avg}$  Average long term slant path in the precipitation 
${L}_{eff}$  Effective path length 
${L}_{G}$  Horizontal projection length in the precipitation 
${L}_{sys}$  System loss at the receiver and transmitter 
${L}_{H}$  Projected pathlength (Table 4) 
l  Link distance (m) 
L  Losses due to the presence of atmospheric gases, clouds, and fogs 
${N}_{eff}$  Effective number of rain cells (Table 4) 
N  Number of tips [Equation (10)] 
${P}_{\tau min}$  Probability of the mean rainfall rate is exceeded for $\tau $min 
${P}_{1min}$  Probability of the mean rainfall rate is exceeded for 1min 
${P}_{t}$  Transmitter power expressed in dBm) 
$\overline{R}$  Average rainfall rate 
$r\left(p\right)$  Rain rate adjustment 
$R\left(p\right)$  Rain rate exceeded for p% of an average year 
${R}_{0}$  Boundary rain rate 
${R}_{M}$  Local peak rainfall rate 
${R}_{max}\left(p\right)$  Maximum rain rate for p% of an average year 
${r}_{p}$  Path length reduction factor [Equation (13)] 
${R}_{p}$  Point rainfall rate [Equation (10)] 
${R}_{p}$  Point rainfall rate exceeded at $p\%$ of the time [Equation (13)] 
${{R}_{rms}}^{2}$  Root mean square (RMS) of rainfall rate 
${R}_{tip}$  Rainfall per tip (mm) [Equation (10)] 
${R}_{1}$, ${R}_{2}$  Rainfall rate 
T  Noise temperature (K) of the system which is assumed to be 290 K 
T  Time gap in consecutive tips [Equation (10)] 
${T}_{a}^{\prime \prime}$  Under rainy conditions temperature 
${T}_{a}^{\prime}$  Under clear sky temperature 
${TR}_{T}$  Maximum rainfall in mm for time interval Tmin 
u  Empirical constant (Table 5) 
v (m/s)  Advection velocity of rain cells 
${x}_{0}$  Location of the ground station 
${x}_{0},{y}_{0}$  Rain cell gravity center 
${Z}_{rain}$  Reflected signal in rainy condition 
${Z}_{th}$  Reflected signal in clear sky condition 
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Ref.  Survey Concentrations 

[14]  The results show that rain attenuation in horizontal polarization is slightly larger than that in vertical polarization. A differential couplingbased compensation was recommended to reduce the rain attenuation effects on polarization in the depolarization processes. 
[15]  In this survey, the artificialneuralnetworkbased models were classified based on input parameters. In addition, the accuracy of the artificialneuralnetworkbased models was accessed through a comparative study. 
[16]  Rain attenuation in a satellite system is more severe than in a terrestrial system, and for a good model, it should be implemented into the model through local climatic elements. 
Factors  Earth–Space  Terrestrial 

Rain  ✓  ✓ 
Cloud, sky noise, scintillation, latitude, Earth radius  ✓  ✗ 
Hop length  Varies according to orbit:
 Varies according to necessity:

Path length reduction  Effective slant path  Effective terrestrial path 
Ref.  Mechanism  Symbol Meanings 

[35]  $\left\{\begin{array}{ccc}{H}_{0}\hfill & \left(\mathrm{km}\right)\hfill & R\le 10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \\ {H}_{0}+log(R/10)\hfill & \left(\mathrm{km}\right)\hfill & R>10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \end{array}\right.$  ${H}_{0}$ is the ${0}^{\circ}$ isotherm height, and R is the rain rate. 
[36]  $10log\left(\frac{{T}_{m}{T}_{a}^{\prime}}{{T}_{m}{T}_{a}^{\prime \prime}}\right)\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\gamma}^{1}$  ${T}_{m}$ is the medium temperature, ${T}_{a}^{\prime}$, under clear sky, and ${T}_{a}^{\u2033}$ is under rainy condition temperatures, and $\gamma $ is the specific attenuation coefficient. 
[37]  $4.5+0.0005{R}^{1.65}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{km}\right)$  R is the rain rate in the range 30–70 mm/h. 
[38]  ${H}_{0}+0.36\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\left(\mathrm{km}\right)$, also using rain height map  ${H}_{0}$ is the ${0}^{\circ}$ isotherm height. 
[32]  $\left\{\begin{array}{cc}4.8,& \left\phi \right\le {30}^{\circ}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{0.277778em}{0ex}}R\le 10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \\ 7.80.1\left\phi \right,& \left\phi \right\ge {30}^{\circ}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{0.277778em}{0ex}}R\ge 10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{h}\hfill \end{array}\right.$  $\phi $ is the latitude in degrees. 
[33]  $\left\{\begin{array}{cc}3+0.028\phi & 0\le \phi <{36}^{\circ}\\ 40.075(\phi {36}^{\circ})& \phi \ge {36}^{\circ}\end{array}\right.$  $\phi $ is the latitude in degrees. 
[34]  $\left\{\begin{array}{cc}4& 0<\left\phi \right<{36}^{\circ}\\ 40.075\left(\left\phi \right{36}^{\circ}\right)& \left\phi \right\ge {36}^{\circ}\end{array}\right.$  $\phi $ is the latitude in degrees. 
[39]  $14.114\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{R}^{0.6402}$  R is the rain rate. 
[40]  $3.6693\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{R}^{0.097}$  R is the rain rate. 
[41]  $\left\{\begin{array}{cccc}50.075(\phi {23}^{\circ})\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}\phantom{\rule{1.em}{0ex}}\phi >{23}^{\circ}\hfill & & \\ 5\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}0\le \phi \le {23}^{\circ}\hfill & & \\ 5\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}0\ge \phi \ge {21}^{\circ}\hfill & & \\ 5+0.1(\phi +{21}^{\circ})\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}{71}^{\circ}\le \phi <{21}^{\circ}\hfill & & \\ 0\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}\phi <{71}^{\circ}\hfill & \end{array}\right.$  $\phi $ is the latitude in degrees. 
Ref.  Mathematical Procedure 

white [35]  ${L}_{eff}=13.367{R}^{0.21}$, where R is the rain rate. 
[42]  ${L}_{eff}=\frac{1}{1+\frac{{L}_{S}cos\theta}{{L}_{G}}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{L}_{S}$, where $\theta $ is the elevation angle, ${H}_{S}$ is the station height above mean sea level of the Earth, and ${L}_{G}$ is the horizontal projection length in the precipitation. 
[43]  ${L}_{eff}=\frac{{L}_{H}{N}_{eff}}{cos\theta}\phantom{\rule{1.em}{0ex}}\left(\mathrm{km}\right)$ where ${L}_{H}$ is the projected pathlength, which is defined by ${R}_{0}$, a boundary rain rate. If $R<{R}_{0}$ then ${L}_{H}=\frac{{H}_{R}{H}_{s}}{tan\theta}\phantom{\rule{4pt}{0ex}}\left(\mathrm{km}\right)$, and if $R\ge {R}_{0}$ then ${L}_{H}=a\left(R\right)\phantom{\rule{4pt}{0ex}}\left(\mathrm{km}\right)$ (Figure 1), and ‘${N}_{eff}$’ is the effective number of rain cells given by ${N}_{eff}\left(\theta ,R\right)={n}_{1}\left(\theta \right)+{n}_{2}\left(\theta \right)\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}R$, where ${n}_{1}\left(\theta \right)=2.38{\theta}^{1.45}+0.82$, and ${n}_{2}\left(\theta \right)=0.01{\theta}^{0.52}+0.09$ ($\theta $ is elevation angle). 
[44]  The estimation of the rain path can be determined by calibrating the reflected signal ${Z}_{th}$ in clearsky conditions and in rainy conditions ${Z}_{rain}$. Once rainfall events are identified the first step of the procedure involves the determination of the volume of the rain cell with ${Z}_{rain}>{Z}_{th}$. 
Ref.  Conversion Techniques 

[49]  Using the Rain rate ${\Gamma}_{\tau}\left(R\right)$, where ${\Gamma}_{\tau}\left(R\right)={P}_{1\mathrm{min}}\left(R\right)/{P}_{\tau \mathrm{min}}\left(R\right)$, the model can convert rain between 1 and $\tau $min, where ${P}_{1\mathrm{min}}$ is the probability that the mean rainfall rate is exceeded for a 1 min accumulation time, and ${P}_{\tau \mathrm{min}}$ is the probability that the mean rainfall rate is exceeded for $\tau $ min accumulation time. 
[50]  Using cumulative rainfall distributions, the model can convert rain between 1 and $\tau $min. 
[51]  Using the conversion factor ${R}_{1}\left(P\right)/{R}_{60}\left(P\right)={CF}_{60}$, where ($C{F}_{60}=a{P}^{b}+c{e}^{\left(d\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}P\right)}$) the model can convert 60 min to a 1 min integration time rain rate, where $C{F}_{60}$ is the conversion factor, a, b, c, d are constants, and P is the probability of rainfall rate exceedance within $0.001\%\le P\le 1\%$. It can also be used to convert between different rain rates [52]. 
[53]  Using the equation (${P}_{1}=1.71\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{P}_{\tau}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{10}^{\left(0.242\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}exp(\tau /2428)\right)}$), $\tau $ min to 1 min conversion. 
[54]  Using the equation ${R}_{1\mathrm{min}}={\left({R}_{\tau \mathrm{min}}\right)}^{d}$, where $d=0.987{\left(\tau \right)}^{0.061}$ the model can convert the rain rate from $\tau $ min to 1 min. 
[55]  Using the equation, $log\left[{R}_{1\mathrm{min}}\left(P\right)]={\alpha}_{r}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}log[{R}_{\tau \mathrm{min}}\left(P\right)\right]$, where ${\alpha}_{r}$: regression component determined statistically, and $5.0\%\le P\le 0.01\%$. 
[56]  In the absence of accurate longterm rainfall data, this method takes the percent of time exceedance, latitude, and longitude as input to generate a 1 min integration time rain rate. 
[57]  The model simply calculates the rain rate $R=60\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{TR}_{T}/T$, where ${TR}_{T}$: maximum rainfall in mm for time interval T min. 
[58]  ${P}_{1}\left(R\right)=\left({a}_{1}/{a}_{t}\right){R}^{\left(b{b}_{1}\right)}exp\left[\left({u}_{t}{u}_{1}\right)R\right]{P}_{t}\left(R\right)$, R: rain rate, u: empirical constant, a, b: depending on the location and integration time of the rain gauge. 
[59]  ${R}_{0.01\%}=\frac{ln\left(0.03\beta \frac{M}{T}\right)}{0.03}$ where M is the average annual rainfall (mm), and T is the number of hours in the year during which rain rates exceed R (mm/h). 
[60]  ${R}_{p}={a}_{p}{M}^{{b}_{p}}{\beta}^{{c}_{p}}$ where p is the percentage of the time, M is the total annual rainfall accumulation, ${a}_{p}$, ${b}_{p}$ and ${c}_{p}$ are constants, which can be derived from $x=log\left(P\right)$, and $\beta $ is the thunderstorm ratio ($\beta ={M}_{1}/{M}_{1}+{M}_{2}$), where ${M}_{1}$ is the rain rate due to a thunderstorm and ${M}_{2}$ is the rain rate without a thunderstorm. 
[61]  ${R}_{0.001\phantom{\rule{4.pt}{0ex}}\mathrm{initial}\phantom{\rule{4.pt}{0ex}}}=23.50390{R}^{0.27896}\phantom{\rule{0.166667em}{0ex}}\mathrm{and}\phantom{\rule{0.166667em}{0ex}}{\beta}^{0.34162}$${R}_{0.01\phantom{\rule{4.pt}{0ex}}\mathrm{initial}\phantom{\rule{4.pt}{0ex}}}=3.69786{R}^{0.46613}{\beta}^{0.43482}$ where R is the rain rate in mm/h and $\beta $ is the regional climatic parameter. 
Parameter  Monoaxial Rain Cell  Biaxial Rain Cell 

Peak rainfall rate (${R}_{M}$)  ✓  ✓ 
Cell radius/radii  ${\rho}_{0}$  ${\rho}_{x},{\rho}_{y}$ 
Tpe  Ref.  Slant or Both  Rain Structure  Rainfall Rate  Frequency  Angle(Earth Station)  Rain Height  Melting Layer Height  Time Series 

EMPI  [32]  Slant  ✓  ✓  ✓  ✓  ✗  ✓  ✓ 
[33]  Slant  ✗  ✓  ✓ ${}^{\u2021}$  ✓$\phantom{\rule{3.33333pt}{0ex}}{}^{\u22cf}$  ✓  ✗  ✗  
[34]  Slant  ✓  ✓  ✓  ✓  ✓  ✗  ✗  
[66]  Slant  ✓  ✓  ✓  ✓ ${}^{\diamond}$  ✓  ✓  ✓  
[68]  Slant  ✓ ${}^{\u25c3}$  ✗  ✗  ✗  ✓  ✓  ✗  
[88]  Slant  ✓  ✓  ✗  ✓  ✓ ${}^{\u25b9}$  ✗  ✗  
[29]  Slant  ✗  ✓  ✓ ${}^{\u2021}$  ✓  ✓  ✗  ✗  
[89]  Both  ✗ ${}^{\u22c9}$  ✓  ✓  ✓ ${}^{\u22ca}$  ✗  ✗  ✗  
[12]  Slant  ✗  ✓  ✓ ${}^{\u2021}$  ✓ ${}^{\u2021}$  ✓  ✗ ${}^{\u22c9}$  ✗  
STAT  [90]  Slant  ✗  ✓  ✓ ${}^{\u22ba}$  ✗  ✗  ✗  ✗ 
[91]  Slant  ✗  ✓  ✓  ✓  ✓  ✗  ✓  
[45]  Slant  ✗  ✓  ✓  ✓  ✓  ✗  ✗  
[92]  Slant  ✗  ✓  ✓ ${}^{\cap}$  ✓ ${}^{\cap}$  ✗  ✗  ✗  
[93]  Slant  ✗  ✗ ${}^{\cup}$  ✗  ✗  ✗  ✗  ✓  
PHY  [37]  Slant  ✓  ✓  ✓  ✓  ✓  ✗  ✗ 
[94]  Both  — ${}^{\u22d7}$  ✓  — ${}^{\sqcap}$  ✓  ✓  ✗  ✗  
[95]  Both  ✓ ${}^{\u25c3}$  ✓  ✗  ✓  ✓  ✓  ✓  
[62]  Slant  ✓  ✓  ✓  ✓  ✓  ✓  ✗  
FADE  [96]  Slant  ✗  ✗  ✓  ✓  ✗  ✗  ✗ 
[97]  Slant  ✗  ✗  ✗  ✗  ✗  ✗  ✓  
[98]  Slant  ✗  ✗  ✓ ${}^{\bigsqcup}$  ✓  ✗  ✗  ✗  
[99]  Slant  ✗  ✗  — ${}^{\oplus}$  ✓ ${}^{\ominus}$  ✗  ✗  ✗  
LB  [100]  Slant  ✓  ✓  ✓  ✓  ✓  ✓  ✓ 
Type  Ref.  Frequency Range  Polarization  Regional Climatic Parameter  Spatial Friendly  Reported Region that Suits 

EMPI  [32]  10–35 GHz  ✓  ✓  ✓  The USA, Europe, and Japan 
[33]  4–6 GHz  NM ${}^{\nparallel}$  Rainfall rate  ✗  Singapore  
[34]  NM  ✓  4 coefficient constants called a,b,c and d depend on geographic area  NM  Best suited areas are in Europe, the USA, Japan, and Australia  
[66]  10–100 GHz  ✓Circular, horizontal and vertical  Rainfall rate  ✗  Temperate region  
[68]  Above 11 GHz  ✗  Local rainfall rate  No information available  No practical information; test information is limited within DBSG3 databank  
[88]  10–20 GHz  NM  Rainfall rate, the probabilities of occurrence and mean rainfalls, for cell and debris  The model considers a single volume rainfalling area and does not consider convective (cell) and stratified rain (debris)  CCIR rain zone  
[29]  10.7–13 GHz (Ku band)  ✓  Rainfall rate  NM  Fiji  
[89]  Terrestrial: 7–137 GHz  ✓k and $\alpha $  Rainfall rate  ✓  Worldwide (ITUR databank)  
[12]  10–30 GHz  Both  Rainfall rate  ✗  Tropical  
STAT  [90]  NM  ✓  Rainfall rate  ✗  Temperate region 
[91]  10–50 GHz  ✓  Climate characteristics, link elevation angle  Has spatial dynamics of rainfall rate parameter due to Van de Kamp [127]  Xi’an, China  
[45]  Up to 55 GHz  ✓  Rainfall rate  ✗  Worldwide  
[92]  NM (only 20 GHz is mentioned)  NM  NM  Information NM  France  
[93]  NM  ✓Horizontal  Measured rain attenuation  NM  Kolkata, India  
PHY  [37]  Reported frequencies are 15, 30, 39.6 GHz  NM  ✓  Rainfall rate is not a function of distance  Temperate and tropical 
[94]  1–100 GHz  ✗  Cell and debris parameter  No spatial correlation function is included  Temperate region  
[95]  11.6 GHz (Range NM)  ✓Circular, Linear  Rainfall rate, wind velocity  ✓(1year rainfall rate PDF was used)  Italy  
[62]  10–50 GHz  ✓  Rainfall rate; rain height; melting layer height, etc.  ✓Vertical and horizontal  Worldwide  
FADE  [96]  Kuband  RHCP, Linear polarization  ✗  ✗  Japan (lowelevation Earth–space path) 
[97]  NM  Horizontal  ✓  ✗  Tropical area  
[98]  10–50 GHz  NM  ✓ ${}^{\bowtie}$  ✗  Designed for global perspective  
[99]  10.982 GHz (Kuband)  Vertical  sparameter ${}^{\u22a1}$  ✗  Malaysia  
LB  [100]  NM  NM  Local rainfall data: it needs to train the BPNN networks  NM  Butare, Rwanda 
Type  Ref.  Used/Validation Databank  Remarks about Validation  Complexity Level  Constraints 

EMPI  [32]  62 experiments in the USA, Japan and Europe  Shows better prediction with minimum 2 years rainfall datasets  low  The operating frequency range is limited to 10–35 GHz 
[33]  INTELSAT POR experiment (Singapore)  The results have been validated with CCIR model and measured attenuation  low  The recommended frequency is limited to 4–6 GHz  
[34]  77 satellite links placed in Europe, the USA, Japan, and Australia (CCIR data bank)  Validated by the author  low  The model is suitable for prediction with an elevation angle ranging from 10${}^{\circ}$ to 40${}^{\circ}$  
[66]  ITUR databank  ITUR databank is used to examine the behavior of m parameter at different frequencies as well as different sites  low  Not spatial friendly  
[68]  DBSG3 databank  The RMS value show that the new model provides the smallest rms and STD in all percentages of time except at 0.001%  high  Application area is limited by low latitudes (between 36${}^{\circ}$ South and 36${}^{\circ}$ North) and low elevation angles (25${}^{\circ}$<)  
[88]  CCIR rain zone with different elevation angle  Validated by the author  medium ∔  10–20 GHz  
[29]  Used 6 tropical city’s rain databanks from ITUR  The experimental result agreed about correction factor induced attenuation especially at elevation angle less than 60${}^{\circ}$ compared to ITUR model  medium  In this model it is assumed that rain is uniformly distributed inside a rain cell  
[89]  ITUR databank  The model gives decent results with the correctness of its terrestrial and slant direction  medium  The model was not checked with actual data for attenuation  
[12]  ✗  Verified with the the beacon signals from WINDS and GE23 satellites (2009 to 2012)  low  Up to 30 GHz frequency is examined  
STAT  [90]  ✗  Not validated with heavy rainfall or with rainfall data around the world for different sites  low  The model is applicable only during the rain periods because no transition is included in the model to switch from rainy to clear sky conditions 
[91]  Validated based on the measured rain attenuation data at Xi’an, China  The validation is a good agreement between measured and predicted attenuation using this model, but has not been compared with other important rain attenuation models  high  The size of the area is not defined for a specific set of parameters  
[92]  ✗  Not validated  —  The probabilistic weather forecasts could be beneficial to maximize the economic value accounting the transmitted data for higher frequencies (say 50 GHz).  
[93]  ✗: used measured attenuation data  The validation shows a good agreement between measured and predicted attenuation using this model, but has not been compared with other important rain attenuation models  medium  It needs to derive mean and standard deviation of the Gaussian distribution for a different geographic area and find the coefficients of secondorder polynomials from real measured attenuation  
PHY  [37]  ✓  Validated at Lae, Papua New Guinea  low  — 
[94]  Satellite: validated through CCIR procedure. Terrestrial: 35 terrestrial paths around the world  Both satellite and terrestrial links have been verified  high ${}^{\u2020}$  The probabilities of incidence and mean precipitation for cells and debris are difficult to determine  
[95]  Experimental dataset  The experimental results show that the method show less error probability.  medium  Needs 1 min rainfall rate  
[62]  DBSG3 databank  Although the model does not outperform the existing ITUR model (approximately 2.4% error), it supports a few additional facilities (e.g., site diversity) and takes account of the interference due to hydrometer scattering  high  The correctness is limited by the local values of input parameters like the melting layer and the rain plateau value, which might not be available everywhere  
FADE  [96]  Experimental dataset  Validated with  low  — 
[97]  ✗  Validated in Kolkata, India, with experimental setup  low  To use fade margin data it needs to remove tropospheric scintillation  
[99]  Only experimental dataset  The resulted output agrees with the measured standard deviation of attenuation  low  The method was tested only at 10.982 GHz  
[98]  NM  Validated in [140,141]  low  Applicable for limited elevation angle 5–60${}^{\circ}$  
LB  [100]  Durban, South Africa  The model was not validated with standard DSDB3 or CCIR rain databanks  —  The model was not tested with established wellknown rain databanks like DBSG3 or CCIR 
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