# A Continuous Multisite Multivariate Generator for Daily Temperature Conditioned by Precipitation Occurrence

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Multivariate Precipitation Occurrence (Dry–Wet)

#### 2.2. Multivariate Maximum and Minimum Temperature

#### 2.3. Evidence for the Goodness of Fit

#### 2.4. Generation of Multivariate Synthetic Series

#### 2.5. Study Area

^{2}. Information regarding the zone was obtained from the official website of the confederation (www.chj.es). The most relevant surface runoff is the Jucar River, which captures the surface runoff of all sub-basins [66]. The most significant reservoirs are Alarcon (1088 hm

^{3}) and Contreras (852 hm

^{3}). The river rises from the Tragacete (1600 ms.n.m) and subsequently arrives at reservoirs Toba, Alarcon, Molinar, and Tous. The study area’s limit ends where the Mediterranean Sea is reached (Figure 2). Rainfall in the Jucar River Basin has decreased since 1980 [67,68]. Temporal and spatial variation characteristics of meteorological elements in the Jucar River Basin are presented in Appendix A (Figure A1, Figure A2, Figure A3 and Figure A4).

## 3. Results

#### 3.1. Multivariate Occurrence Synthetic Series

#### 3.2. Stochastic Multisite Multivariate Temperature Series

#### 3.3. Generation of Multivariate Synthetic Temperature Series

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Spatial distribution of annual (

**a**) maximum temperature (°C) and (

**b**) temperature range (°C).

**Figure A2.**Spatial distribution of annual (

**a**) precipitation occurrence (wet days/year) and (

**b**) rainfall (mm/year).

**Figure A3.**Interannual variation trends of the average (

**a**) maximum temperature (°C) and (

**b**) temperature range (°C).

**Figure A4.**Interannual variation trends of the average (

**a**) precipitation occurrence (wet days year

^{−1}) and (

**b**) rainfall (mm year

^{−1}).

**Figure A5.**Daily correlation function for residual series considering the ten lag days: (

**a**) Model 1 (M1) and (

**b**) Model 2 (M2).

## References

- Sivakumar, B. Chaos in Hydrology: Bridging Determinism and Stochasticity, 1st ed.; Springer Science: Dordrecht, The Netherlands, 2017; pp. 63–111. [Google Scholar]
- Beneyto, C.; Aranda, J.Á.; Benito, G.; Francés, F. New Approach to Estimate Extreme Flooding Using Continuous Synthetic Simulation Supported by Regional Precipitation and Non-Systematic Flood Data. Water
**2020**, 12, 3174. [Google Scholar] [CrossRef] - Chang, F.; Hsu, K.; Chang, L. Flood Forecasting Using Machine Learning Methods. Water
**2019**, 2, 14–53. [Google Scholar] [CrossRef] - Chang, F.J.; Guo, S. Advances in Hydrologic Forecasts and Water Resources Management. Water
**2020**, 12, 1819. [Google Scholar] [CrossRef] - Gabriel, K.R.; Neumann, J. A Markov Chain model for daily rainfall occurrence at tel aviv. Q. J. R. Meteorol. Soc.
**1962**, 88, 90–95. [Google Scholar] [CrossRef] - Caskey, E. A Markov Chain model for the probability of precipitation occurrence in intervals of various length. Mon. Weather Rev.
**1963**, 91, 298–301. [Google Scholar] [CrossRef] - Matalas, N.C. Time Series Analysis, 4th ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 1967; Volume 3. [Google Scholar] [CrossRef]
- Todorovic, P.; Woolhiser, D.A. A Stochastic Model of n -Day Precipitation. J. Appl. Meteorol.
**1975**, 14, 17–24. [Google Scholar] [CrossRef] - Richardson, C.W. Stochastic Simulation of Daily Precipitation, Temperature, and Solar Radiation. Water Resour. Res.
**1981**, 17, 182–190. [Google Scholar] [CrossRef] - Roldán, J. Tendencias Actuales En El Modelado de La Precipitación Diaria. Ing. Agua
**1994**, I, 89–100. [Google Scholar] [CrossRef] - Rajagopalan, B.; Lall, U.; Tarboton, D.G. Nonhomogeneous Markov Model for Daily Precipitation. J. Hydrol. Eng.
**1996**, 1, 33–40. [Google Scholar] [CrossRef] - Wilks, D.S. Multisite Generalization of a Daily Stochastic Precipitation Generation Model. J. Hydrol.
**1998**, 210, 178–191. [Google Scholar] [CrossRef] - Wilks, D.S.S.; Wilby, R.L.L. The Weather Generation Game: A review of stochastic weather models. Prog. Phys. Geogr.
**1999**, 23, 329–357. [Google Scholar] [CrossRef] - Harrold, T.I. A Nonparametric Model for Stochastic Generation of Daily Rainfall Amounts. Water Resour. Res.
**2003**, 39, 1–12. [Google Scholar] [CrossRef] - Brissette, F.P.; Khalili, M.; Leconte, R. Efficient Stochastic Generation of Multi-Site Synthetic Precipitation Data. J. Hydrol.
**2007**, 345, 121–133. [Google Scholar] [CrossRef] - Liu, Y.; Zhang, W.; Shao, Y.; Zhang, K. A comparison of four precipitation distribution models used in daily stochastic models. Adv. Atmos. Sci.
**2011**, 28, 809–820. [Google Scholar] [CrossRef] - Li, C.; Singh, V.P.; Mishra, A.K. Simulation of the entire range of daily precipitation using a hybrid probability distribution. Water Resour. Res.
**2012**, 48, 1–17. [Google Scholar] [CrossRef] - Mehrotra, R.; Li, J.; Westra, S.; Sharma, A. A programming tool to generate multi-site daily rainfall using a two-stage semi parametric model. Environ. Model. Softw.
**2015**, 63, 230–239. [Google Scholar] [CrossRef] - So, B.J.; Kwon, H.H.; Kim, D.; Lee, S.O. Modeling of daily rainfall sequence and extremes based on a semiparametric pareto tail approach at multiple locations. J. Hydrol.
**2015**, 529, 1442–1450. [Google Scholar] [CrossRef] - Wilks, D.S. Simultaneous stochastic simulation of daily precipitation, temperature and solar radiation at multiple sites in complex terrain. Agric. For. Meteorol.
**1999**, 96, 85–101. [Google Scholar] [CrossRef] - Semenov, M.A.; Barrow, E.M. LARS-WG A Stochastic Weather Generator for Use in Climate Impact Studies LARS-WG: Stochastic Weather Generator Contents, Harpenden, Hertfordshire, United Kigdom. Available online: http://resources.rothamsted.ac.uk/sites/default/files/groups/mas-models/download/LARS-WG-Manual.pdf (accessed on 10 December 2021).
- Chen, J.; Brissette, F.P.; Leconte, R. WeaGETS—A Matlab-Based Daily Scale Weather Generator for Generating Precipitation and Temperature. Procedia Environ. Sci.
**2012**, 13, 2222–2235. [Google Scholar] [CrossRef] - Salas, J.J.D.; Delleur, J.W.; Yevjevich, V.M.; Lane, W.L. Applied Modeling of Hydrologic Time Series; Water Resources Publication: Littleton, CO, USA, 1980; ISBN 0-918334-37-3. [Google Scholar]
- Srikanthan, R.; McMahon, T.A. Stochastic generation of annual, monthly and daily climate data: A review. Hydrol. Earth Syst. Sci.
**2001**, 5, 653–670. [Google Scholar] [CrossRef] - Qian, B.; Gameda, S.; Hayhoe, H.; De Jong, R.; Bootsma, A. Comparison of LARS-WG and AAFC-WG Stochastic Weather Generators for Diverse Canadian Climates. Clim. Res.
**2004**, 26, 175–191. [Google Scholar] [CrossRef] - Flecher, C.; Naveau, P.; Allard, D.; Brisson, N. A stochastic daily weather generator for skewed data. Water Resour. Res.
**2010**, 46, 1–15. [Google Scholar] [CrossRef] - Hayhoe, H.N. Improvements of stochastic weather data generators for diverse climates. Clim. Res.
**2000**, 14, 75–87. [Google Scholar] [CrossRef] - Ailliot, P.; Allard, D.; Monbet, V.; Naveau, P. Stochastic Weather Generators: An Overview of Weather Type Models. J. Société Française Stat.
**2015**, 156, 101–113. [Google Scholar] - Richardson, C.W.; Wright, D.A.; Nofziger, D.L.; Hornsby, A.G. WGEN: A Model for Generating Daily Weather Variables. ARS
**1984**, 8, 1–83. [Google Scholar] - Carter, T.; Posch, M.; Tuomenvirta, H. SILMUSCEN and CLIGEN User’s Guide: Guidelines for the Construction of Climatic Scenarios and Use of a Stochastic Weather Generator in the Finnish. Available online: https://www.osti.gov/etdeweb/biblio/458148 (accessed on 5 November 2021).
- Stöckle, C.O.; Nelson, R.; Donatelli, M.; Castellvì, F. ClimGen: A flexible weather generation program. In Proceedings of the 2nd International Symposium Modelling Cropping Systems, Florence, Italy, 17 July 2001. [Google Scholar]
- Marcello, D.; Gianni, B.; Ephrem, H.; Simone, B.; Roberto, C.; Bettina, B. CLIMA: A Weather Generator Framework. In Proceedings of the 18th World IMACS/MODSIM Congress, Carins, Australia, 13–17 July 2009; Available online: https://core.ac.uk/download/pdf/38616113.pdf (accessed on 17 July 2009).
- Foufoula-georgiou, E.; Lettenmaier, D.P. A Markov renewal model for rainfall occurrences. Water Resour. Res.
**1987**, 23, 875–884. [Google Scholar] [CrossRef] - Bárdossy, A.; Pegram, G.G.S. Copula Based Multisite Model for Daily Precipitation Simulation. Hydrol. Earth Syst. Sci.
**2009**, 13, 2299–2314. [Google Scholar] [CrossRef] - Sansom, J. A Hidden Markov Model for Rainfall Using Breakpoint Data. J. Clim.
**1998**, 11, 42–53. [Google Scholar] [CrossRef] - Ailliot, P.; Thompson, C.; Thomson, P. Space-Time Modelling of Precipitation by Using a Hidden Markov Model and Censored Gaussian Distributions. J. R. Stat. Soc. Ser. C Appl. Stat.
**2009**, 58, 405–426. [Google Scholar] [CrossRef] - Racsko, P.; Szeidl, L.; Semenov, M. A serial approach to local stochastic weather models. Ecol. Model.
**1991**, 57, 27–41. [Google Scholar] [CrossRef] - Zheng, X.; Katz, R.W. Mixture Model of Generalized Chain-Dependent Processes and Its Application to Simulation of Interannual Variability of Daily Rainfall. J. Hydrol.
**2008**, 349, 191–199. [Google Scholar] [CrossRef] - Hannachi, A. Intermittency, Autoregression and Censoring: A First-Order AR Model for Daily Precipitation. Meteorol. Appl.
**2014**, 21, 384–397. [Google Scholar] [CrossRef] - Khan, R.S.; Abul, M.; Bhuiyan, E.; Khan, R.S.; Bhuiyan, M.A.E.; García-Ortega, E.; Rigo, T. Artificial Intelligence-Based Techniques for Rainfall Estimation Integrating Multisource Precipitation Datasets. Atmosphere
**2021**, 12, 1239. [Google Scholar] [CrossRef] - Chiang, Y.M.; Chang, F.J.; Jou, B.J.D.; Lin, P.F. Dynamic ANN for Precipitation Estimation and Forecasting from Radar Observations. J. Hydrol.
**2007**, 334, 250–261. [Google Scholar] [CrossRef] - Cachim, P. ANN Prediction of Fire Temperature in Timber. J. Struct. Fire Eng.
**2019**, 10, 233–244. [Google Scholar] [CrossRef] - Li, X.; Li, Z.; Huang, W.; Zhou, P. Performance of Statistical and Machine Learning Ensembles for Daily Temperature Downscaling. Theor. Appl. Climatol.
**2020**, 140, 571–588. [Google Scholar] [CrossRef] - Bochenek, B.; Ustrnul, Z. Machine Learning in Weather Prediction and Climate Analyses—Applications and Perspectives. Atmosphere
**2022**, 13, 180. [Google Scholar] [CrossRef] - Oses, N.; Azpiroz, I.; Marchi, S.; Guidotti, D.; Quartulli, M.; Olaizola, I.G. Analysis of Copernicus’ Era5 Climate Reanalysis Data as a Replacement for Weather Station Temperature Measurements in Machine Learning Models for Olive Phenology Phase Prediction. Sensors
**2020**, 20, 6381. [Google Scholar] [CrossRef] - Hernández-Bedolla, J.; Solera, A.; Paredes-Arquiola, J.; Pedro-Monzonís, M.; Andreu, J.; Sánchez-Quispe, S. The Assessment of Sustainability Indexes and Climate Change Impacts on Integrated Water Resource Management. Water
**2017**, 9, 213. [Google Scholar] [CrossRef] - Tang, Y.; Zeng, G.; Yang, X.; Iyakaremye, V.; Li, Z. Intraseasonal Oscillation of Summer Extreme High Temperature in Northeast China and Associated Atmospheric Circulation Anomalies. Atmosphere
**2022**, 13, 387. [Google Scholar] [CrossRef] - Yang, Q. Extended-Range Forecast for the Low-Frequency Oscillation of Temperature and Low-Temperature Weather over the Lower Reaches of the Yangtze River in Winter. Chin. J. Atmos. Sci.
**2021**, 45, 21–36. [Google Scholar] [CrossRef] - Chen, J.; Brissette, F.P.; Leconte, R. A Daily Stochastic Weather Generator for Preserving Low-Frequency of Climate Variability. J. Hydrol.
**2010**, 388, 480–490. [Google Scholar] [CrossRef] - Hansen, J.W.; Mavromatis, T. Correcting Low-Frequency Variability Bias in Stochastic Weather Generators. Agric. For. Meteorol.
**2001**, 109, 297–310. [Google Scholar] [CrossRef] - Chen, J.; Arsenault, R.; Brissette, F.P.; Côté, P.; Su, T. Coupling Annual, Monthly and Daily Weather Generators to Simulate Multisite and Multivariate Climate Variables with Low—Frequency Variability for Hydrological Modelling. Clim. Dyn.
**2019**, 53, 3841–3860. [Google Scholar] [CrossRef] - Apipattanavis, S.; Podestá, G.; Rajagopalan, B.; Katz, R.W. A Semiparametric Multivariate and Multisite Weather Generator. Water Resour. Res.
**2007**, 43, W11401. [Google Scholar] [CrossRef] - Li, X.; Babovic, V. A New Scheme for Multivariate, Multisite Weather Generator with Inter-Variable, Inter-Site Dependence and Inter-Annual Variability Based on Empirical Copula Approach. Clim. Dyn.
**2019**, 52, 2247–2267. [Google Scholar] [CrossRef] - Ghosh Dastidar, A.; Ghosh, D.; Dasgupta, S.; De, U.K. Higher Order Markov Chain Models for Monsoon Rainfall over West Bengal, India. Indian J. Radio Space Phys.
**2010**, 39, 39–44. [Google Scholar] - Hosseini, R.; Le, N.; Zidek, J. Selecting a Binary Markov Model for a Precipitation Process. Environ. Ecol. Stat.
**2011**, 18, 795–820. [Google Scholar] [CrossRef] - Lennartsson, J.; Baxevani, A.; Chen, D. Modelling Precipitation in Sweden Using Multiple Step Markov Chains and a Composite Model. J. Hydrol.
**2008**, 363, 42–59. [Google Scholar] [CrossRef] - Otienoongála, J.; Ster, D.; Stern, R. Extending Genstat Capability to Analyze Rainfall Data Using a Markov Chain Model. Eur. Sci. J. August Ed.
**2012**, 8, 1857–7881. [Google Scholar] - Chen, J.; Brissette, F.P. Stochastic Generation of Daily Precipitation Amounts: Review and Evaluation of Different Models. Clim. Res.
**2014**, 59, 189–206. [Google Scholar] [CrossRef] - Woolhiser, D.A.; Pegram, G.G.S. Maximum Likelihood Estimation of Fourier Coefficients to Describe Seasonal Variations of Parameters in Stochastic Daily Precipitation Models. J. Appl. Meteorol.
**1979**, 18, 34–42. [Google Scholar] [CrossRef] - Keller, D.E.; Fischer, A.M.; Frei, C.; Liniger, M.A.; Appenzeller, C.; Knutti, R. Implementation and Validation of a Wilks-Type Multi-Site Daily Precipitation Generator over a Typical Alpine River Catchment. Hydrol. Earth Syst. Sci.
**2015**, 19, 2163–2177. [Google Scholar] [CrossRef] - Chen, J.; Brissette, F.P. Comparison of Five Stochastic Weather Generators in Simulating Daily Precipitation and Temperature for the Loess Plateau of China. Int. J. Climatol.
**2014**, 34, 3089–3105. [Google Scholar] [CrossRef] - Sakia, R.M. The Box-Cox Transformation Technique: A review. J. R. Stat. Soc.
**1992**, 41, 169–178. [Google Scholar] [CrossRef] - Anderson, R.L. Distribution of the Serial Correlation Coefficient. Ann. Math. Stat.
**1942**, 13, 1–13. [Google Scholar] [CrossRef] - Moors, D. Stubblebine Chi-Square Tests for multivariate normality with application to common Stock prices. Comun. Stat. -Theory Methods
**1981**, 10, 713–738. [Google Scholar] [CrossRef] - Hu, S. Akaike Information Criterion Statistics. Math. Comput. Simul.
**1987**, 29, 452. [Google Scholar] [CrossRef] - Pedro-Monzonís, M.; Ferrer, J.; Solera, A.; Estrela, T.; Paredes-Arquiola, J. Key Issues for Determining the Exploitable Water Resources in a Mediterranean River Basin. Sci. Total Environ.
**2015**, 503–504, 319–328. [Google Scholar] [CrossRef] - Pérez-Martín, M.A.; Thurston, W.; Estrela, T.; del Amo, P. Cambio En Las Series Hidrológicas de Los Últimos 30 Años y Sus Causas. El Efecto 80. III Jorn. Ing. Agua (JIA 2013). La Protección Contra Los Riesgos Hídricos
**2013**, 2, 527–534. [Google Scholar] - CHJ Plan Hidrológico de La Demarcación Hidrográfica Del Júcar, Memoria-Anejo 2. CJH, Valencia, España. 2015. Available online: https://www.chj.es/es-es/medioambiente/planificacionhidrologica/Paginas/PHC-2015-2021-Plan-Hidrologico-cuenca.aspx (accessed on 10 December 2021).
- Herrera, S.; Fernández, J.; Gutiérrez, J.M. Update of the Spain02 Gridded Observational Dataset for EURO-CORDEX Evaluation: Assessing the Effect of the Interpolation Methodology. Int. J. Climatol.
**2016**, 36, 900–908. [Google Scholar] [CrossRef] - Daly, C. Guidelines for Assessing the Suitability of Spatial Climate Data Sets. Int. J. Climatol.
**2006**, 26, 707–721. [Google Scholar] [CrossRef] - Pérez-Martín, M.A.; Estrela, T.; Andreu, J.; Ferrer, J.; Pérez-Martín, M.A.; Andreu, J.; Estrela, T.; Ferrer, J. Modeling Water Resources and River-Aquifer Interaction in the Júcar River Basin, Spain. Water Resour. Manag.
**2014**, 28, 4337–4358. [Google Scholar] [CrossRef] - Melsen, L.; Teuling, A.; Torfs, P.; Zappa, M.; Mizukami, N.; Clark, M.; Uijlenhoet, R. Representation of Spatial and Temporal Variability in Large-Domain Hydrological Models: Case Study for a Mesoscale Pre-Alpine Basin. Hydrol. Earth Syst. Sci.
**2016**, 20, 2207–2226. [Google Scholar] [CrossRef] - Parlange, M.B.; Katz, R.W.; Parlange, M.B.; Katz, R.W. An Extended Version of the Richardson Model for Simulating Daily Weather Variables. J. Appl. Meteorol.
**2000**, 39, 610–622. [Google Scholar] [CrossRef]

**Figure 1.**Proposed methodology for multisite multivariate precipitation occurrence, daily and annual temperatures.

**Figure 3.**Fourier series and confidence limits for Alarcon: (

**a**) ${p}_{01}$ (

**b**) ${p}_{11}$ with four parameters. Confidence limits at 95% (lower and upper limits).

**Figure 4.**Skewness coefficient (daily average) of normalized series (66 years): (

**a**) maximum temperature and (

**b**) temperature range. Anderson confidence limits (95%).

**Figure 5.**Fourier series (daily average) of maximum temperature series (66 years): (

**a**) mean wet days, (

**b**) mean dry days, (

**c**) standard deviation wet days, and (

**d**) standard deviation dry days.

**Figure 6.**Fourier series (daily average) of temperature range series (66 years): (

**a**) mean wet days, (

**b**) mean dry days, (

**c**) standard deviation wet days, and (

**d**) standard deviation dry days.

**Figure 7.**Theoretical normal distribution (blue) and histogram for residual series for all sub-basins: (

**a**) Model 1 (maximum temperature) and (

**b**) Model 2 (temperature range).

**Figure 8.**Scatter plots for rainfall occurrence (mean 66 years observed and 1000 simulated series) for the five sub-basins: (

**a**) daily mean for each calendar day (green) and (

**b**) monthly mean for each calendar moth (green) for M1 and M2.

**Figure 9.**Scatter plots for observed mean versus generated temperature (mean 66 years observed and 1000 simulated series) for two models: (

**a**) maximum temperature for each calendar day (blue) and (

**b**) temperature range for each calendar day (red).

**Figure 10.**Scatter plots for observed standard deviations versus generated (mean 66 years observed and 1000 simulated series) for two models: (

**a**) maximum temperature for each calendar day (blue) and (

**b**) temperature range for each calendar day (red).

**Figure 11.**Scatter plots for observed skewness coefficient versus generated (mean 66 years observed and 1000 simulated series) for two models: (

**a**) maximum temperature for each calendar day (blue) and (

**b**) temperature range for each calendar day (red).

**Figure 12.**Monthly temperature for all sub-basins (mean 66 years observed and 1000 simulated series) observed and simulated for (

**a**) maximum temperature for each month (blue) and (

**b**) temperature range for each month (red), for 66 years, 5 sub-basins, and all months.

**Figure 13.**Yearly temperature for all sub-basins observed (obs) and simulated (sim) for (

**a**) maximum temperature and (

**b**) temperature range. (1) Alarcon, (2) Contreras, (3) Molinar, (4) Tous, and (5) Huerto Mulet. The outliers are plotted individually using the ‘+’ marker symbol.

Sub-Basin | Wet Day Threshold (mm) | |||
---|---|---|---|---|

0.001 * | 0.01 | 0.10 | 0.25 | |

Alarcon | −590.2 | −515.3 | −362.2 | −310.9 |

Contreras | −681.5 | −551.2 | −459.5 | −421.3 |

Molinar | −562.3 | −420.7 | −261.2 | −215.1 |

Tous | −587.4 | −463.6 | −380.5 | −340.0 |

Huerto Mulet | −610.5 | −554.7 | −467.3 | −427.3 |

Model | Statistical/Sub-Basin | Alarcon | Contreras | Molinar | Tous | Huerto Mulet |
---|---|---|---|---|---|---|

1 * | Mean | −6.7 × 10^{−5} | −2.0 × 10^{−4} | 7.5 × 10^{−5} | −2.6 × 10^{−4} | 5.6 × 10^{−5} |

Deviation | 0.842 | 0.821 | 0.834 | 0.812 | 0.850 | |

Skewness coefficient | −0.185 | −0.242 | −0.245 | −0.089 | 0.026 | |

Lag-one autocorrelation | 0.005 | 0.003 | 0.009 | −0.041 | −0.042 | |

AIC | −8369 | −9508 | −8814 | −10,152 | −7958 | |

2 ** | Mean | −3.09 × 10^{−4} | −5.98 × 10^{−4} | −6.83 × 10^{−5} | −2.70 × 10^{−4} | −2.65 × 10^{−4} |

Deviation | 0.937 | 0.920 | 0.942 | 0.900 | 0.942 | |

Skewness coefficient | −0.009 | −0.038 | −0.044 | 0.112 | −0.028 | |

Lag-one autocorrelation | 0.036 | 0.043 | −0.030 | −0.082 | −0.039 | |

AIC | −6471 | −8233 | −5957 | −10,294 | −5896 |

Parameter | Model 1 (M1) | Model 2 (M2) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |

RMSE (°C/day) | 1.881 | 1.107 | 1.392 | 1.156 | 0.767 | 1.786 | 1.019 | 1.290 | 1.078 | 0.780 |

MAE (°C/day) | 1.503 | 0.820 | 1.092 | 0.896 | 0.572 | 1.455 | 0.773 | 1.021 | 0.852 | 0.582 |

PE (%) | 0.043 | 0.027 | 0.017 | 0.031 | 0.021 | 0.035 | 0.049 | 0.040 | 0.025 | 0.012 |

Maximum Temperature Cross-Correlation | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Sub-Basin | Alarcon | Contreras | Molinar | Tous | Huerto M | * Alarcon | * Contreras | * Molinar | * Tous | * Huerto M |

Alarcon | 1.000 | 1.000 | ||||||||

Contreras | 0.833 | 1.000 | 0.834 | 1.000 | ||||||

Molinar | 0.760 | 0.797 | 1.000 | 0.765 | 0.819 | 1.000 | ||||

Tous | 0.239 | 0.492 | 0.598 | 1.000 | 0.243 | 0.489 | 0.610 | 1.000 | ||

Huerto M | 0.223 | 0.371 | 0.390 | 0.802 | 1.000 | 0.230 | 0.377 | 0.398 | 0.800 | 1.000 |

Temperature Range Cross-Correlation | ||||||||||

Sub-Basin | Alarcon | Contreras | Molinar | Tous | Huerto M | * Alarcon | * Contreras | * Molinar | * Tous | * Huerto M |

Alarcon | 1.000 | 1.000 | ||||||||

Contreras | 0.719 | 1.000 | 0.718 | 1.000 | ||||||

Molinar | 0.891 | 0.592 | 1.000 | 0.895 | 0.590 | 1.000 | ||||

Tous | 0.563 | 0.494 | 0.754 | 1.000 | 0.565 | 0.499 | 0.759 | 1.000 | ||

Huerto M | 0.504 | 0.331 | 0.710 | 0.918 | 1.000 | 0.502 | 0.333 | 0.708 | 0.917 | 1.000 |

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**MDPI and ACS Style**

Hernández-Bedolla, J.; Solera, A.; Paredes-Arquiola, J.; Sanchez-Quispe, S.T.; Domínguez-Sánchez, C. A Continuous Multisite Multivariate Generator for Daily Temperature Conditioned by Precipitation Occurrence. *Water* **2022**, *14*, 3494.
https://doi.org/10.3390/w14213494

**AMA Style**

Hernández-Bedolla J, Solera A, Paredes-Arquiola J, Sanchez-Quispe ST, Domínguez-Sánchez C. A Continuous Multisite Multivariate Generator for Daily Temperature Conditioned by Precipitation Occurrence. *Water*. 2022; 14(21):3494.
https://doi.org/10.3390/w14213494

**Chicago/Turabian Style**

Hernández-Bedolla, Joel, Abel Solera, Javier Paredes-Arquiola, Sonia Tatiana Sanchez-Quispe, and Constantino Domínguez-Sánchez. 2022. "A Continuous Multisite Multivariate Generator for Daily Temperature Conditioned by Precipitation Occurrence" *Water* 14, no. 21: 3494.
https://doi.org/10.3390/w14213494