CN107545121A - A kind of Soil Temperature And Moisture data assimilation method based on EnPF - Google Patents

A kind of Soil Temperature And Moisture data assimilation method based on EnPF Download PDF

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CN107545121A
CN107545121A CN201710889554.5A CN201710889554A CN107545121A CN 107545121 A CN107545121 A CN 107545121A CN 201710889554 A CN201710889554 A CN 201710889554A CN 107545121 A CN107545121 A CN 107545121A
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付晓雷
余钟波
蒋晓蕾
鞠琴
吕海深
金保明
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Fuzhou University
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Abstract

The present invention provides a kind of Soil Temperature And Moisture data assimilation method based on EnPF, and it comprises the following steps：Step 1：By analyzing Ensemble Kalman Filter and particle filter, the weight thought in particle filter is applied in Ensemble Kalman Filter, establishes the set particle filter of dual sampling；Based on weight size, sample degeneracy situation is judged, if sample degeneracy, reject the minimum particle of weight and weighted average is asked to residual particles, in analysis phase resampling；If particle retains the predicted value of all particles and corresponding weight, in the predicted value of analysis phase more new particle without degeneration；Step 2：With reference to land-surface hydrological processes, Soil Temperature And Moisture data assimilation is carried out, summarizes Soil Temperature And Moisture simulated profile.The weight thought of particle filter is used in Ensemble Kalman Filter by the present invention, and ad hoc hypothesis is not done in the distribution to observation error, carries out the land face hydrographic data assimilation of Soil Temperature And Moisture, improves the simulation precision of model.

Description

A kind of Soil Temperature And Moisture data assimilation method based on EnPF
Technical field
The invention belongs to land face hydrologic forecast to predict field, and in particular to a kind of Soil Temperature And Moisture data assimilation based on EnPF Method.
Background technology
Under the conditions of Global climate change, gradually rising for global average temperature always is Jiao of concern in the last hundred years Point.The rise of global average temperature, inevitably result in the change of the soil moisture.However, the soil moisture can not only influence farming The growth production of thing, meanwhile, it is also the part during the energy variation of climatic model, Meteorological Models underlying surface.Accurately The soil moisture forecast, can be not only incubated for the irrigations of crops, earth's surface and a rational directive function be provided, can also improved Weather, the precision of weather forecast.In addition, the change of the soil moisture can also cause the reallocation of soil moisture, and soil moisture is A key factor in water circulation.Soil moisture accuracy of the forecast can not only influence the forecast of flood, for agricultural irrigation Plan, weather weather forecast etc. also have an impact.Therefore, soil temperature and humidity in the hydrology, agricultural and meteorology all with important angle Color.Data assimilation method can merge multi-source information into land-surface hydrological processes, reduce simulation error, improve soil temperature and humidity Simulation precision.
Nearest decades, data assimilation method as the technological means of a great development prospect experienced empirical method, Optimize a process of interpolation, continuation method and alphabetic data assimilation method.The development of data assimilation method is for improving weather Pattern, Meteorological Models, the forecast precision of state variable of land surface model provide an effective way, are acknowledged as changing and pass System hydrology, a key technology for building Hydrology.But data assimilation method will have certain vacation in application process If condition, however, these conditions almost do not meet practical study situation.In addition, though data assimilation method can improve model Forecast precision, but the rule for the assimilation system established according to researcher is different, and assimilation method is in some moment, Mou Xiekong Between position may can not significantly improve the forecast precision of model.Therefore, it is how same come data by loosening assumed condition Change method, this not only turn into hydrology discipline development requirement, and weather, meteorological subject and ocean subject problem encountered it One.At present, the assimilation method of actual conditions is not complied fully with also.
The content of the invention
In order to solve the deficiencies in the prior art, the present invention provides a kind of Soil Temperature And Moisture data assimilation method based on EnPF, By analyzing the principle of Ensemble Kalman Filter (EnKF) and particle filter (PF), the weight thought of particle filter is used In Ensemble Kalman Filter, so as to loosen the error assumed condition of Ensemble Kalman Filter, (distribution of observation error does not rehearse If), this assumed condition of reserving model error Gaussian distributed, land-surface hydrological process simulation is carried out, improve the mould of model Intend precision.
The present invention uses following technical scheme：A kind of Soil Temperature And Moisture data assimilation method based on EnPF, it is characterised in that： Comprise the following steps：Step 1：By analyzing Ensemble Kalman Filter and particle filter, by the weight in particle filter Thought is applied in Ensemble Kalman Filter, establishes the set particle filter of dual sampling；Based on weight size, judge that particle moves back Change situation, if sample degeneracy, reject the minimum particle of weight and weighted average is asked to residual particles, adopted again in the analysis phase Sample；If particle retains the predicted value of all particles and corresponding weight, in the predicted value of analysis phase more new particle without degeneration； Step 2：With reference to land-surface hydrological processes, Soil Temperature And Moisture data assimilation is carried out, summarizes Soil Temperature And Moisture simulated profile.
In an embodiment of the present invention, step 1 specifically includes following steps：
Step 1：N number of particle is randomly selected under given probability distributionAnd corresponding weight 1/N；
Step 2：The predicted value of each particle of t is obtained using state equation (1)
Xt=Y (Xt-1)+Vt-1 (19)
Zt=H (Xt)+Ut (20)
Wherein, XtIt is the state variable of t；ZtIt is the measurement vector of t, system mode and observation is passed through into observation Operator H is connected；VtAnd UtIt is t state vector and the independent identically distributed error of measurement vector respectively；Y () is particle Function；
When there is observation, the weight at t-1 moment is updated using equation (3) and (4) to obtain the weight of tThe threshold epsilon of given weight, is determined whetherParticle, i.e., whether particle degenerates, and goes to Step 3；If without observation, weight does not update, and Step 2 is repeated, at the time of having observation to occur；
WeightCalculation formula it is as follows：
In formula, R is the variance of observation error,
Based on formula (3), the weight calculation formula after resampling is as follows：
In formula,Fix (X) is that X is rounded to 0 direction；
Step3：If there is particle to degenerate, it will forecast that weight corresponding to stage remaining particle normalizes first, and ask Weighted averageM≤N,Resampling is carried out under Gaussian Profile and obtains the new grain of t SubgroupAnd recalculate weight using equation (3) and (4), will if particle is not degenerated The predicted value of the particle obtained in Step2 and corresponding weight retain；Using the Ensemble Kalman Filter algorithm of weighting, to forecast ValueCarry out state renewal, obtains state estimation；
Step4：Based on obtained state estimation under given probability distribution, particle assembly is reselectedCorresponding weight is 1/N, makes t=t+1, returns to Step 2.
Compared with prior art, the present invention has advantages below：The weight thought of particle filter is used to gather Kalman In filtering, ad hoc hypothesis is not done in the distribution to observation error, is carried out the land face hydrographic data assimilation of Soil Temperature And Moisture, is improved model Simulation precision.
Brief description of the drawings
Fig. 1 is a kind of Soil Temperature And Moisture data assimilation method flow chart based on EnPF of the present invention；
Fig. 2 is the result figure that KENMet websites assimilate topsoil temperature in real time；
Fig. 3 is the result figure that certain KENMet website assimilates a topsoil temperature daily；
Fig. 4 is the result figure that certain KENMet website assimilates remotely-sensed data MODIS LST.
Embodiment
Explanation is further explained to the present invention with specific embodiment below in conjunction with the accompanying drawings.
The present invention provides a kind of Soil Temperature And Moisture data assimilation method based on EnPF, and it comprises the following steps：
Step 1：By analyzing Ensemble Kalman Filter and particle filter, by the weight thought in particle filter It is applied in Ensemble Kalman Filter, establishes the set particle filter of dual sampling；Based on weight size, sample degeneracy feelings are judged Condition, if sample degeneracy, reject the minimum particle of weight and weighted average is asked to residual particles, in analysis phase resampling；If Particle retains the predicted value of all particles and corresponding weight, in the predicted value of analysis phase more new particle without degeneration；
Step 2：With reference to land-surface hydrological processes, Soil Temperature And Moisture data assimilation is carried out, summarizes Soil Temperature And Moisture simulated profile.
Wherein step 1 specifically includes following steps：
Step 1：N number of particle is randomly selected under given probability distributionAnd corresponding weight 1/N；
Step 2：The predicted value of each particle of t is obtained using state equation (1)
Xt=Y (Xt-1)+Vt-1 (23)
Zt=H (Xt)+Ut (24)
Wherein, XtIt is the state variable of t；ZtIt is the measurement vector of t, system mode and observation is passed through into observation Operator H is connected；VtAnd UtIt is t state vector and the independent identically distributed error of measurement vector respectively；Y () is particle Function；
When there is observation, the weight at t-1 moment is updated using equation (3) and (4) to obtain the weight of tThe threshold epsilon of given weight, is determined whetherParticle, i.e. whether particle degenerate；And go to Step 3；If without observation, weight does not update, and Step 2 is repeated, at the time of having observation to occur；
WeightCalculation formula it is as follows：
In formula, R is the variance of observation error,
Based on formula (3), the weight calculation formula after resampling is as follows：
In formula,Fix (X) is that X is rounded to 0 direction；
Step3：If there is particle to degenerate, it will forecast that weight corresponding to stage remaining particle normalizes first, and ask Weighted averageM≤N,Resampling is carried out under Gaussian Profile and obtains the new grain of t SubgroupAnd recalculate weight using equation (3) and (4), will if particle is not degenerated The predicted value of the particle obtained in Step2 and corresponding weight retain；Using the Ensemble Kalman Filter algorithm of weighting, to forecast ValueCarry out state renewal, obtains state estimation；
Step4：Based on obtained state estimation under given probability distribution, particle assembly is reselectedCorresponding weight is 1/N, makes t=t+1, returns to Step 2, asks for the forecast of the particle of subsequent time Value.
Further, using the Ensemble Kalman Filter algorithm of weighting in Step3, to predicted valueCarry out state renewal, Obtain state estimation, including step in detail below：
Wherein KtIt is kalman gain matrix, expression formula is as follows：
Wherein prediction error conarianceCalculation formula be：
Wherein：
Then the estimate of t state is as follows：
The error covariance of analysis phase is as follows：
In formula,It is the set of the state variable vector of renewal,It is caused measuring assembly.
In an embodiment of the present invention, if measurement is the linear combination of state variable, i.e.,Then：
In an embodiment of the present invention, if measurement is the nonlinear combination of state variable,WithUtilize Equation below calculates：
Wherein：
In the specific embodiment of the invention 1：
Land-surface hydrological processes select general land-surface model CLM as modeling operator, carry out the Simulation prediction of soil moisture.Figure (2-4) show respectively carries out real-time assimilation table using EnPF to website soil moisture observation and remotely-sensed data MODIS LST The layer soil moisture, daily topsoil temperature of assimilation and the assimilation experiments for assimilating remotely-sensed data MODIS LST.Fig. 2 tables Bright EnPF can significantly improve the simulation precision of model, become once a day from real time when assimilating frequency, although assimilation effect becomes Difference, but still can improve the analog result of model.For assimilation remotely-sensed data (Fig. 4), EnPF assimilation effect with daily The effect of topsoil temperature of assimilation is more or less the same.As a result show in addition to bottommost layer, the assimilation method passes through assimilation Multi-source data can improve model accuracy.Specific error result is as follows：
The soil moisture analogue value and assimilation number and observation of the different assimilation experiment of corresponding 3 of the KENMet websites of table 1 Between root-mean-square error (K).Measured value (when), measured value (day), MODIS (original) corresponds to 3 assimilation experiments respectively.
Ensemble Kalman Filter requires model and observation error Gaussian distributed, but land-surface hydrological processes are generally difficult to Meet this hypothesis.The present invention establishes a kind of set particle filter EnPF of dual sampling, loosens mistake by analyzing EnKF and PF Poor assumed condition, assimilate multi-source information, improve modeling precision.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (6)

  1. A kind of 1. Soil Temperature And Moisture data assimilation method based on EnPF, it is characterised in that：Comprise the following steps：
    Step 1：By analyzing Ensemble Kalman Filter and particle filter, by the weight thought application in particle filter Into Ensemble Kalman Filter, the set particle filter of dual sampling is established；Based on weight size, sample degeneracy situation is judged, If sample degeneracy, reject the minimum particle of weight and weighted average is asked to residual particles, in analysis phase resampling；If particle Without degeneration, retain the predicted value of all particles and corresponding weight, in the predicted value of analysis phase more new particle；
    Step 2：With reference to land-surface hydrological processes, Soil Temperature And Moisture data assimilation is carried out, summarizes Soil Temperature And Moisture simulated profile.
  2. 2. the Soil Temperature And Moisture data assimilation method according to claim 1 based on EnPF, it is characterised in that：Step 1 is specific Comprise the following steps：
    Step1：N number of particle is randomly selected under given probability distributionAnd corresponding weight 1/N；
    Step2：The predicted value of each particle of t is obtained using state equation (1)
    Xt=Y (Xt-1)+Vt-1 (1)
    Zt=H (Xt)+Ut (2)
    Wherein, XtIt is the state variable of t；ZtIt is the measurement vector of t, system mode and observation is passed through into Observation Operators H Connect；VtAnd UtIt is t state vector and the independent identically distributed error of measurement vector respectively；Y () is particle function； When there is observation, the weight at t-1 moment is updated using equation (3) and (4) to obtain the weight of tIt is given The threshold epsilon of weight, is determined whetherParticle, i.e. whether particle degenerates, and goes to Step 3；If do not see Measured value, weight do not update, and Step 2 are repeated, at the time of having observation to occur；
    WeightCalculation formula it is as follows：
    <mrow> <msubsup> <mi>w</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mfrac> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>0.5</mn> <mo>/</mo> <mi>R</mi> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>Z</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>H</mi> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>0.5</mn> <mo>/</mo> <mi>R</mi> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>Z</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>H</mi> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    In formula, R is the variance of observation error,
    Based on formula (3), the weight calculation formula after resampling is as follows：
    <mrow> <msubsup> <mi>w</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>s</mi> </mrow> <mi>i</mi> </msubsup> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>Nw</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>-</mo> <mi>f</mi> <mi>i</mi> <mi>x</mi> <mrow> <mo>(</mo> <msubsup> <mi>Nw</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>l</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    In formula,Fix (X) is that X is rounded to 0 direction；
    Step3：If there is particle to degenerate, it will forecast that weight corresponding to stage remaining particle normalizes first, and ask weighting It is averageCarrying out under Gaussian Profile resampling, to obtain t new PopulationAnd recalculate weight using equation (3) and (4), will if particle is not degenerated The predicted value of the particle obtained in Step2 and corresponding weight retain；Using the Ensemble Kalman Filter algorithm of weighting, to forecast ValueCarry out state renewal, obtains state estimation；
    Step4：Based on obtained state estimation under given probability distribution, particle assembly is reselectedCorresponding weight is 1/N, makes t=t+1, returns to Step 2.
  3. 3. the Soil Temperature And Moisture data assimilation method according to claim 2 based on EnPF, it is characterised in that：It is sharp in Step3 With the Ensemble Kalman Filter algorithm of weighting, to predicted valueCarry out state renewal, obtain state estimation, including following tool Body step：
    <mrow> <msubsup> <mi>X</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>+</mo> <msub> <mi>K</mi> <mi>t</mi> </msub> <mo>&amp;lsqb;</mo> <msubsup> <mi>Z</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>-</mo> <mover> <mrow> <mi>H</mi> <mo>&amp;lsqb;</mo> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    Wherein KtIt is kalman gain matrix, expression formula is as follows：
    <mrow> <msub> <mi>K</mi> <mi>t</mi> </msub> <mo>=</mo> <msubsup> <mi>P</mi> <mi>t</mi> <mi>f</mi> </msubsup> <msup> <mi>H</mi> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>HP</mi> <mi>t</mi> <mi>f</mi> </msubsup> <msup> <mi>H</mi> <mi>T</mi> </msup> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Wherein prediction error conarianceCalculation formula be：
    <mrow> <msubsup> <mi>P</mi> <mi>t</mi> <mi>f</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <msub> <mi>E</mi> <mi>t</mi> </msub> <msubsup> <mi>E</mi> <mi>t</mi> <mi>T</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：
    <mrow> <msub> <mi>E</mi> <mi>t</mi> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mn>1</mn> </msubsup> <mo>-</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>N</mi> </msubsup> <mo>-</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>w</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>s</mi> </mrow> <mi>i</mi> </msubsup> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Then the estimate of t state is as follows：
    <mrow> <msubsup> <mi>X</mi> <mi>t</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msubsup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>w</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>r</mi> <mi>e</mi> <mi>s</mi> </mrow> <mi>i</mi> </msubsup> <msubsup> <mi>X</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    The error covariance of analysis phase is as follows：
    <mrow> <msubsup> <mi>E</mi> <mi>t</mi> <mi>a</mi> </msubsup> <mo>=</mo> <mo>&amp;lsqb;</mo> <msubsup> <mi>X</mi> <mrow> <mi>t</mi> <mo>,</mo> <mn>1</mn> </mrow> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>X</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>N</mi> </mrow> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mrow> <mi>u</mi> <mi>p</mi> </mrow> </msubsup> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>P</mi> <mi>t</mi> <mi>a</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <msubsup> <mi>E</mi> <mi>t</mi> <mi>a</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>E</mi> <mi>t</mi> <mi>a</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    In formula,It is the set of the state variable vector of renewal,It is caused measuring assembly.
  4. 4. the Soil Temperature And Moisture data assimilation method according to claim 3 based on EnPF, it is characterised in that：If measurement is shape The linear combination of state variable, i.e.,Then：
    <mrow> <mo>&amp;lsqb;</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mn>1</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>N</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mi>A</mi> <mo>&amp;lsqb;</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mn>1</mn> </msubsup> <mo>-</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>N</mi> </msubsup> <mo>-</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mi>t</mi> <mi>f</mi> </msubsup> <msup> <mi>H</mi> <mi>T</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>-</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mi>A</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <msub> <mi>E</mi> <mi>t</mi> </msub> <msubsup> <mi>E</mi> <mi>t</mi> <mi>T</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>HP</mi> <mi>t</mi> <mi>f</mi> </msubsup> <msup> <mi>H</mi> <mi>T</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mi>A</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <msub> <mi>E</mi> <mi>t</mi> </msub> <msubsup> <mi>E</mi> <mi>t</mi> <mi>T</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  5. 5. the Soil Temperature And Moisture data assimilation method according to claim 3 based on EnPF, it is characterised in that：If measurement is shape The nonlinear combination of state variable, thenWithCalculated using equation below：
    <mrow> <msubsup> <mi>P</mi> <mi>t</mi> <mi>f</mi> </msubsup> <msup> <mi>H</mi> <mi>T</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>-</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>HP</mi> <mi>t</mi> <mi>f</mi> </msubsup> <msup> <mi>H</mi> <mi>T</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>H</mi> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：
    <mrow> <mi>H</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>H</mi> <mo>&amp;lsqb;</mo> <msubsup> <mi>X</mi> <mi>t</mi> <mi>i</mi> </msubsup> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
  6. 6. the Soil Temperature And Moisture data assimilation method according to claim 1 based on EnPF, it is characterised in that：Land face water Literary model uses general land-surface model CLM.
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CN110309481A (en) * 2019-04-24 2019-10-08 武汉大学 Agricultural land soil kinetics process model modeling method
CN110321917A (en) * 2019-04-24 2019-10-11 武汉大学 The farm field data assimilation method of printenv

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110309481A (en) * 2019-04-24 2019-10-08 武汉大学 Agricultural land soil kinetics process model modeling method
CN110321917A (en) * 2019-04-24 2019-10-11 武汉大学 The farm field data assimilation method of printenv

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