CN117649133B - Prediction method and system for large reservoir water surface evaporation - Google Patents
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Abstract
The invention discloses a prediction method and a prediction system for water surface evaporation of a large reservoir, which belong to the field of water resources and atmospheric climate, and comprise the following steps: fitting water-gas temperature difference functions under different wind speed orders based on a target large reservoir, obtaining saturated water vapor pressure according to a Pengman formula, and constructing a reservoir water surface evaporation model; based on Nash efficiency coefficient NSE, carrying out parameter calibration on the water surface evaporation model by utilizing a particle swarm algorithm, and optimizing the water surface evaporation model of the reservoir; predicting the water surface evaporation of the target large-scale reservoir according to the optimized reservoir water surface evaporation model; the method fully considers the influence of the temperature difference of water and gas and the change wind speed on the estimation and prediction of the water surface evaporation capacity, has the characteristics of firm theoretical basis, higher simulation precision and the like, and provides technical support for reservoir water resource planning and reasonable configuration.
Description
Technical Field
The invention relates to the field of water resources and atmospheric climate, in particular to a prediction method and a prediction system for water surface evaporation of a large reservoir.
Background
The evaporation of the water surface of the reservoir is an important component part of the water balance of a large-scale reservoir, and is closely related to water ecology, comprehensive benefits of the reservoir, water resource utilization and the like. The reservoir water storage operation changes the climate environment of a local area of a reservoir area to a certain extent, so that a mathematical model for evaluating and predicting the water surface evaporation is constructed, and the method has great significance for grasping the change rule of the reservoir water quantity and scientifically developing the operation scheduling of the water conservancy junction.
The reservoir water surface evaporation calculation model in the present stage has low simulation precision due to the lack of research on the temperature difference of water and air and the internal association of the temperature difference and the air speed. The existing model mainly considers the influences of saturated water vapor pressure difference, average relative humidity and wind speed, ignores the water vapor temperature difference reflecting the climate of a specific region and the climate effect of a specific water body, does not reveal the internal close connection between the local wind speed and the water vapor temperature difference, and is difficult to accurately describe the change rule of water surface evaporation and main meteorological factors.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a novel prediction technology for large-scale reservoir water surface evaporation, and the relationship between the influence degree of the water-air temperature difference on the evaporation coefficient and the wind speed is explored by exploring the influence factor of the large-scale reservoir water surface evaporation so as to simulate and predict the water surface evaporation capacity of the large-scale reservoir more accurately and provide technical support for reasonable utilization and scientific management of water resources of the large-scale reservoir.
In order to achieve the technical purpose, the application provides a prediction method for large-scale reservoir water surface evaporation, which comprises the following steps:
based on a target large reservoir, a reservoir water surface evaporation model is constructed by fitting water-air temperature difference functions under different wind speed magnitudes and obtaining saturated water vapor pressure according to a Pengman formula;
based on Nash efficiency coefficient NSE, parameter calibration is carried out on the water surface evaporation model by utilizing a particle swarm algorithm, and the water surface evaporation model of the reservoir is optimized;
and predicting the water surface evaporation of the target large-scale reservoir according to the optimized reservoir water surface evaporation model.
Preferably, in the process of obtaining the water-air temperature difference function, according to the prediction area and the prediction period of the target large reservoir, water surface evaporation and meteorological data of the target large reservoir are collected, the prediction period is divided into a rate period and a verification period, and then the water surface evaporation and meteorological data of the corresponding prediction period are respectively divided into two parts of the rate period and the verification period, so that parameters of the constructed water surface evaporation model of the reservoir are calibrated, and the optimized water surface evaporation model of the reservoir is verified.
Preferably, in the process of verifying the optimized water surface evaporation model of the reservoir, based on the optimized water surface evaporation model of the reservoir, the water surface evaporation capacity is simulated according to data corresponding to the verification period, and a Nash efficiency coefficient NSE and a root mean square error RMSE between the simulated water surface evaporation capacity and the actually measured water surface evaporation capacity are obtained, so that the optimized water surface evaporation model of the reservoir is verified.
Preferably, in the process of fitting the water-air temperature difference functions under different wind speed orders, the wind speed is divided into different sections according to the actual range of the wind speed, and in the different wind speed sections, the power function relation between the evaporation coefficient of the water surface and the absolute value of the water-air temperature difference is fitted, so that the water-air temperature difference functions under different wind speed orders are determined.
Preferably, in the process of fitting the water-air temperature difference function at different wind speed magnitudes, the water-air temperature difference function is expressed as:in which A n 、B n 、C n N=1 to N, which is a constant; delta T is the temperature difference of water and air; u is wind speed; u (U) n Segmenting points for wind speed; n is the number of wind speed segments.
Preferably, in the process of obtaining the saturated water vapor pressure, the saturated water vapor pressure is calculated according to a penman formula by replacing the average air temperature with the water temperature at 0.5m of the reservoir surface of the target large reservoir, and the saturated water vapor pressure is expressed as:wherein a and b are constants; e, e z Is saturated water vapor pressure; e is the actual water vapor pressure; t (T) s0.5 Water temperature at 0.5m of the warehouse surface.
Preferably, in the process of constructing the reservoir water surface evaporation model, the reservoir water surface evaporation model is expressed as:wherein c and d are constants;to simulate evaporation from the water surface; r is the average relative humidity.
Preferably, in the process of parameter calibration of the water surface evaporation model, based on the reservoir water surface evaporation model, the parameter calibration is performed on the water surface evaporation model by using a particle swarm algorithm according to Nash efficiency coefficient NSE through water surface evaporation and meteorological data corresponding to the calibration, and a parameter a, b, c, d value in a formula is solved, wherein when the Nash efficiency coefficient NSE is larger than 0.5, the model simulation precision meets the requirement.
The invention discloses a prediction system for large-scale reservoir water surface evaporation, which comprises:
the model construction module is used for constructing a reservoir water surface evaporation model based on a target large reservoir by fitting a water-air temperature difference function under different wind speed magnitudes and obtaining saturated water vapor pressure according to a Pengman formula;
the model optimization module is used for carrying out parameter calibration on the water surface evaporation model by utilizing a particle swarm algorithm based on a Nash efficiency coefficient NSE and optimizing the water surface evaporation model of the reservoir;
and the prediction module is used for predicting the water surface evaporation of the target large-scale reservoir according to the optimized water surface evaporation model of the reservoir.
Preferably, the system further comprises a data acquisition module, which is used for collecting water surface evaporation and meteorological data of the target large reservoir according to a prediction area and a prediction period of the target large reservoir, dividing the prediction period into a rate period and a verification period, dividing the water surface evaporation and meteorological data of the corresponding prediction period into two parts of the rate period and the verification period respectively, carrying out parameter calibration on the constructed water surface evaporation model of the reservoir, and verifying the optimized water surface evaporation model of the reservoir, wherein based on the optimized water surface evaporation model of the reservoir, the water surface evaporation capacity is simulated according to data corresponding to the verification period, a Nash efficiency coefficient NSE and a root mean square error RMSE between the simulated water surface evaporation capacity and the actually measured water surface evaporation capacity are obtained, and the optimized water surface evaporation model of the reservoir is verified.
The system selects each historical meteorological data as model input, based on a deep learning algorithm, realizes the prediction of each meteorological factor through the steps of training, setting optimal parameters and the like, and predicts the evaporation capacity of the water surface of the reservoir by utilizing the predicted value of the meteorological factor.
The invention discloses the following technical effects:
the method can fully consider the influence of the temperature difference of water and air, the change wind speed and the water temperature of the reservoir surface on the water surface evaporation capacity, has a clear physical mechanism, improves the accuracy of estimating the water surface evaporation capacity of the reservoir, and provides technical support for estimating and predicting the water surface evaporation of the reservoir.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a process for constructing a reservoir water surface evaporation model according to an embodiment of the invention;
fig. 2 is a schematic diagram showing the results of actual measurement of water surface evaporation capacity and simulated evaporation capacity of a large reservoir from 2013, 8 months, 2022, 12 months year by year according to an embodiment of the present invention;
fig. 3 is a schematic flow chart of the method according to the invention.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, which are generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, as provided in the accompanying drawings, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present application without making any inventive effort, are intended to be within the scope of the present application.
1-3, a new specific construction process of a reservoir water surface evaporation model is provided for overcoming the defects of the prior estimation technology of reservoir water surface evaporation capacity, and further, the water surface evaporation prediction is carried out through the model, and the method comprises the following steps:
s1, determining a prediction area and a prediction period, and collecting corresponding water surface evaporation and meteorological data, wherein a blank value or an abnormal value of original data is interpolated, the data are processed into data of a required prediction time scale, and the water surface evaporation and meteorological data are respectively divided into two periods of a rate period and a verification period;
in step S1, interpolation is carried out on the weather data vacancy values of the prediction areas in the prediction time periods of the collected corresponding prediction time scales;
determining the predicted time scale data accumulation or average value processing to be corresponding time scale evaporation and meteorological data;
according to the prediction period, dividing the prediction period into two periods of a rate period and a verification period, and dividing the processed water surface evaporation and meteorological data of the corresponding period into two portions of the rate period and the verification period respectively.
S2, constructing a reservoir water surface evaporation model containing water-air temperature difference functions under different wind speed orders;
in step S2, for the water surface evaporation characteristics of the reservoir, fitting the water-air temperature difference functions under different wind speed magnitudes, and the specific formula is as follows:
in which A n 、B n 、C n (n=1 to N) is a constant; delta T is the temperature difference of water and air, and the temperature is lower than the temperature; u is wind speed, m/s; u (U) n The wind speed is segmented to be points, m/s; n is windNumber of speed segments.
Dividing the wind speed into different sections according to the actual wind speed range, fitting a power function relation between a water surface evaporation coefficient (E/delta E) and an absolute value of a water-air temperature difference in the different wind speed sections, and determining a parameter A n 、B n 、C n (n=1 to N) to obtain a water-air temperature difference function f (delta T) under different wind speed magnitudes, wherein E represents the actual evaporation quantity, delta E represents the saturated water-air pressure difference,。
the saturated water vapor pressure is calculated by adopting a Pengman formula, and the water temperature at 0.5m of the reservoir surface is used for replacing the average air temperature, and the specific formula is as follows:wherein a and b are constants; e, e z Saturated water vapor pressure, hpa; e is the actual water vapor pressure, hpa; t (T) s0.5 Water temperature at 0.5m of the warehouse surface, and DEG C.
And establishing a reservoir water surface evaporation model by combining water-air temperature difference functions and saturated water-air pressure formulas under different wind speed orders, wherein the specific formulas are as follows:
a, b, c, d, A in n 、B n 、C n (n=1 to N) is a constant;mm for simulating water surface evaporation; r is the average relative humidity in decimal;is the pressure of the saturated water vapor and is equal to the pressure of the saturated water vapor,the method comprises the steps of carrying out a first treatment on the surface of the e is the actual water vapor pressure, and the water vapor pressure,；T s0.5 water temperature at 0.5m of the warehouse surface, and DEG C; delta T is the temperature difference of water and air, and the temperature is lower than the temperature; u is wind speed, m/s; u (U) n The wind speed is segmented to be points, m/s; n is the wind speed segmentation number。
S3, parameter calibration is carried out on the reservoir water surface evaporation model by utilizing a particle swarm algorithm and a Nash efficiency coefficient;
in step S3, on the basis of the established reservoir water surface evaporation model, combining the rated water surface evaporation and meteorological data divided for corresponding time periods, carrying out parameter calibration on the water surface evaporation model by utilizing a particle swarm algorithm based on Nash efficiency coefficient NSE, solving a parameter a, b, c, d value in a formula, and meeting the requirement of model simulation precision when the Nash efficiency coefficient is larger than 0.5. The particle swarm algorithm and Nash efficiency coefficient principle and calculation formula are as follows:
particle swarm optimization algorithms consider the entire swarm as a group of particles, one particle per bird, based on the principle of swarm bird feeding. Each particle has a running speed that determines the direction and distance the particle moves in the multidimensional search space, which is influenced by the inertia of the particle. In each iteration process, the particle swarm algorithm updates the speed and the position of the particle swarm algorithm through an individual extremum Prest and a global extremum Gbest, and after a preset criterion is met, the particle swarm algorithm jumps out of the iteration to obtain an optimal solution;
in the method, in the process of the invention,the water surface evaporation simulation value;the measured value is the water surface evaporation value;is thatAverage value.
NSE reflects the simulation result of the model, the value is from minus infinity to 1, NSE is close to 1, the simulation is better, and the reliability of the model is high; NSE is much less than 0, the model is not trusted; RMSE reflects how far the analog data deviates from the measured value, with smaller RMSE indicating higher analog accuracy.
S4, verifying the model, and constructing reservoir water surface evaporation models of water-air temperature difference functions under different wind speed orders.
In step S4, combining the verification period water surface evaporation and meteorological data, substituting the a, b, c, d value of the parameter obtained by solving the particle swarm algorithm into the established reservoir water surface evaporation model;
and verifying the reservoir water surface evaporation model, and calculating to obtain Nash efficiency coefficient NSE and root mean square error RMSE of the simulated water surface evaporation capacity and the actually measured water surface evaporation capacity in the verification period, so as to evaluate the precision of the simulation result.
Example 1: taking a certain large reservoir as an example, the technical flow is as shown in fig. 1, and the method is implemented specifically according to the following steps:
(1) And collecting water surface evaporation and meteorological data actually measured day by day in the 2013 8-2022 12-month period of a certain large-scale reservoir floating experimental station, interpolating the blank value or abnormal value of the original data and processing the day by day data into month by day data. Dividing 8 months in 2013 to 12 months in 2019 into regular rate, dividing 1 month in 2020 to 12 months in 2022 into verification period, and dividing month-by-month water surface evaporation and meteorological data of a certain large reservoir floating experiment station 2013 to 12 months in 2022 into two parts of regular rate and verification period respectively.
(2) And constructing a reservoir water surface evaporation model containing water-air temperature difference functions under different wind speed orders. Aiming at the characteristic of small change of the wind speed of a certain large reservoir, dividing the wind speed into three sections, respectively drawing power function relation between the water surface evaporation coefficient (E/delta E) and the absolute value of the water-air temperature difference in the three wind speed sections, and determining the parameter A n 、B n 、C n (n=1 to 3), and the water-air temperature difference function f (delta T) under different wind speed orders is obtained respectively, wherein the specific formula is as follows:
wherein f (delta T) is a water-air temperature difference function, U is wind speed, m/s, delta T is water-air temperature difference and DEG C;
wherein saturated water vapor pressure is calculated by adopting a Pengman formula, wherein the water temperature at 0.5m of the warehouse surface is used for replacing the average air temperature, and the specific formula is as follows:
wherein a and b are constants; e, e z Saturated water vapor pressure, hpa; e is the actual water vapor pressure, hpa; t (T) s0.5 Water temperature at 0.5m of the warehouse surface, and DEG C.
And establishing a reservoir water surface evaporation model by combining a water-air temperature difference function and a saturated water vapor pressure formula under different wind speed magnitudes, wherein the specific formula is as follows:
wherein a, b, c, d is a constant;mm for simulating water surface evaporation; r is the average relative humidity in decimal;is the pressure of the saturated water vapor and is equal to the pressure of the saturated water vapor,the method comprises the steps of carrying out a first treatment on the surface of the e is the actual water vapor pressure, and the water vapor pressure,；T s0.5 water temperature at 0.5m of the warehouse surface, and DEG C; delta T is the temperature difference of water and air, and the temperature is lower than the temperature; u is wind speed, m/s.
(3) On the basis of the established reservoir water surface evaporation model, combining month-by-month water surface evaporation and meteorological data of a large reservoir floating experimental station in the period from 2013 month 8 month to 2019 month 12 month, carrying out parameter calibration on the reservoir water surface evaporation model by utilizing a particle swarm algorithm, solving a parameter a, b, c, d value in the model, and considering that the model rate calibration precision meets the requirement when the Nash efficiency coefficient NSE is larger than 0.5. The calculated model parameters a, b, c, d are respectively 0.36, 1.01, 15.59 and 14.80, and the model rate periodic nse=0.72 and rmse=10.45 meet the precision requirement.
(4) Based on month-by-month water surface evaporation and meteorological data of a large-scale reservoir floating experimental station in a verification period of 1 month-2022 month, model parameters a=0.36, b=1.01, c=15.59 and d=14.80 obtained through solving in the steps are combined and substituted into an established reservoir water surface evaporation model, the water surface evaporation model is verified, nash efficiency coefficients NSE and RMSE of simulated water surface evaporation capacity and actually measured water surface evaporation capacity in the verification period are obtained through calculation, and the model verification period NSE=0.69 and RMSE=12.56 meet the precision requirement.
According to the invention, actually measured meteorological data are collected, the influence of water vapor on evaporation is represented by a water vapor temperature difference function under different wind speed orders is introduced, saturated water vapor pressure difference, water vapor temperature difference and relative humidity are selected as water surface evaporation calculation factors, parameter calibration, model inspection and precision evaluation are carried out by using a particle swarm algorithm, a water surface evaporation calculation model for a large reservoir is provided, and further, water surface evaporation prediction is realized.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In the description of the present invention, it should be understood that the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the present invention, the meaning of "a plurality" is two or more, unless explicitly defined otherwise.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (3)
1. The prediction method for the large-scale reservoir water surface evaporation is characterized by comprising the following steps of:
based on a target large reservoir, a reservoir water surface evaporation model is constructed by fitting water-air temperature difference functions under different wind speed magnitudes and obtaining saturated water vapor pressure according to a Pengman formula;
based on Nash efficiency coefficient NSE, parameter calibration is carried out on the water surface evaporation model by utilizing a particle swarm algorithm, and the water surface evaporation model of the reservoir is optimized;
predicting the water surface evaporation of the target large-scale reservoir according to the optimized reservoir water surface evaporation model;
in the process of acquiring the water-air temperature difference function, according to a predicted area and a predicted period of the target large reservoir, collecting water surface evaporation and meteorological data of the target large reservoir, dividing the predicted period into a rate period and a verification period, dividing the water surface evaporation and meteorological data of the corresponding predicted period into two parts of the rate period and the verification period respectively, and performing parameter calibration on the constructed water surface evaporation model of the reservoir and verification on the optimized water surface evaporation model of the reservoir;
in the process of verifying the optimized water surface evaporation model of the reservoir, based on the optimized water surface evaporation model of the reservoir, simulating water surface evaporation capacity through data corresponding to the verification period, and obtaining Nash efficiency coefficient NSE and root mean square error RMSE between the simulated water surface evaporation capacity and the actually measured water surface evaporation capacity, so as to verify the optimized water surface evaporation model of the reservoir;
in the process of fitting the water-air temperature difference functions under different wind speed orders, dividing wind speeds into different sections according to the actual range of wind speeds, and fitting a power function relation between a water surface evaporation coefficient and an absolute value of the water-air temperature difference in the different wind speed sections to determine the water-air temperature difference functions under different wind speed orders;
in the process of fitting the water-air temperature difference function under different wind speed magnitudes, the water-air temperature difference function is expressed as:in which A n 、B n 、C n N=1 to N, which is a constant; delta T is the temperature difference of water and air; u is wind speed; u (U) n Segmenting points for wind speed; n is the number of wind speed segments;
in the process of obtaining saturated water vapor pressure, replacing average air temperature by water temperature at 0.5m of the reservoir surface of the target large reservoir, and calculating the saturated water vapor pressure according to a Pengman formula, wherein the saturated water vapor pressure is expressed as:wherein a and b are constants; e, e z Is saturated water vapor pressure; e is the actual water vapor pressure; t (T) s0.5 Water temperature at 0.5m of the warehouse surface;
in the process of constructing a reservoir water surface evaporation model, the reservoir water surface evaporation model is expressed as:
wherein c and d are constants; />To simulate evaporation from the water surface; r is the average relative humidity.
2. The method for predicting water surface evaporation for a large reservoir according to claim 1, wherein the method comprises the following steps:
in the process of parameter calibration of the water surface evaporation model, the parameter calibration is carried out on the water surface evaporation model by utilizing a particle swarm algorithm according to Nash efficiency coefficient NSE through the water surface evaporation and meteorological data corresponding to the calibration period based on the water surface evaporation model of the reservoir, a parameter a, b, c, d value in a formula is solved, and when the Nash efficiency coefficient NSE is larger than 0.5, the model simulation precision meets the requirement.
3. A large reservoir surface evaporation-oriented prediction system, comprising:
the model construction module is used for constructing a reservoir water surface evaporation model based on a target large reservoir by fitting a water-air temperature difference function under different wind speed magnitudes and obtaining saturated water vapor pressure according to a Pengman formula;
the model optimization module is used for carrying out parameter calibration on the water surface evaporation model by utilizing a particle swarm algorithm based on a Nash efficiency coefficient NSE and optimizing the water surface evaporation model of the reservoir;
the prediction module is used for predicting the water surface evaporation of the target large-scale reservoir according to the optimized water surface evaporation model of the reservoir;
the system further comprises a data acquisition module, wherein the data acquisition module is used for collecting water surface evaporation and meteorological data of the target large-scale reservoir according to a prediction area and a prediction period of the target large-scale reservoir, dividing the prediction period into a rate period and a verification period, dividing the water surface evaporation and meteorological data of the corresponding prediction period into two parts of the rate period and the verification period respectively, carrying out parameter calibration on the constructed water surface evaporation model of the reservoir, and verifying the optimized water surface evaporation model of the reservoir, wherein based on the optimized water surface evaporation model of the reservoir, the water surface evaporation capacity is simulated through data corresponding to the verification period, a Nash efficiency coefficient NSE and a root mean square error RMSE between the simulated water surface evaporation capacity and the actually measured water surface evaporation capacity are obtained, and the optimized water surface evaporation model of the reservoir is verified;
in the process of fitting the water-air temperature difference functions under different wind speed orders, the system divides wind speed into different intervals according to the actual range of wind speed, and fits a power function relation between the water surface evaporation coefficient and the absolute value of the water-air temperature difference in the different wind speed intervals to determine the water-air temperature difference functions under different wind speed orders;
the system fits different wind speed magnitudesIn the process of the water-gas temperature difference function, the water-gas temperature difference function is expressed as follows:in which A n 、B n 、C n N=1 to N, which is a constant; delta T is the temperature difference of water and air; u is wind speed; u (U) n Segmenting points for wind speed; n is the number of wind speed segments;
in the process of acquiring saturated water vapor pressure, the system replaces the average air temperature by the water temperature at the position of 0.5m of the reservoir surface of the target large reservoir, calculates the saturated water vapor pressure according to a Pengman formula, and the saturated water vapor pressure is expressed as:wherein a and b are constants; e, e z Is saturated water vapor pressure; e is the actual water vapor pressure; t (T) s0.5 Water temperature at 0.5m of the warehouse surface;
in the process of constructing a reservoir water surface evaporation model, the reservoir water surface evaporation model is expressed as:wherein c and d are constants; />To simulate evaporation from the water surface; r is the average relative humidity.
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