parameter optimization - objective function reduction - where to start???

Question

hydrogall 2015-11-13

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https://ww2.mathworks.cn/matlabcentral/answers/254691-parameter-optimization-objective-function-reduction-where-to-start

Hi, I have set up a model to simulate snow-water-equivalent and snowmelt. I would like to calibrate this model to my observed values of snow-water-equivalent. I know that matlab has solvers and parameter optimization tools, but I find the directions/description to be confusing. Where do I even begin with this? How do I establish the respective ranges for the parameters to be calibrated? How should my code be altered to enable parameter optimization?

Thank you for any direction,guidance and help!

      %Degree-day method for snow melting.
      %Data from the ...
      x=load('C:\U....dat'); %Load the file with data
      td=x(:,4);              %hour of the day
      GlobalRad=x(:,5);          %Global Radiation
      T=x(:,6);                %Air Temperature
      P=x(:,7);                %Precipitation
      Snow_obs=x(:,8);           %SWE Observed
      SnowDepth=x(:,9);        %Snow Depth Observed
      ts=x(:,10);                %start time of daylight on day d (t0)
      te=x(:,11);               %end time of daylight on day d (t1)
      dTd=x(:,12);              %difference between the max and min daily temperatures on day d
      snow_sim(1)=0;
      runoff=zeros(length(P));
      %Parameters (TO BE CALIBRATED)
      Scf=1.3;                        %Snowfall correction factor
      TT=1;                          %Threshold temperature
      C=3.5;                           %Degree-day factor (mm day-1 C-1)(Ac)
      B=0.05;         % Factor to convert the temp amplitude into a degree day factor
      %Parameters (USE DEFAULT)
      Cfr=0.05;                        %Refreezing coefficient (use default value of 0.05)
      Cwh=0.1;                         %Water holding capacity (use default value of 0.1)
      snow_sim(1)=0;                   %Simulated snowpack is 0 mm for day 1
      snow_sim_water(1)=0;             %Liquid water in snowpack for day 1 the water is 0 mm
      for t=1 : length(td);       %time series loop
          ln(t)=24-te(t)+ts(t);                    %length of the night
          Z(t)=2*((te(t)-ts(t))/(3.14*ln(t)));        %factor ensuring that daily mean vaules of As equals Ac
          if ts(t)<=td(t)<te(t);
            As(t)=C+(B*dTd(t)*(sin(3.14*((td(t)-ts(t))/(te(t)-ts(t))))));       %equation for time variant degree day factor secnario1
          else As(t)=C-(B*dTd(t)*Z(t));            %equation for time variant degree day factor senario 2
          end
      end
      as=As';         % transpose As from a row to a column vector
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      for t=2 : length(P);             %time series loop
          if T(t)< TT;                 %If the temperature for day t is lower than the threshold value for melting (=below TT degrees) then refreezing of melt water will occur
              refreez(t)=Cfr*as(t)*(TT-T(t));      %Equation for refreezing of meltwater
              if refreez(t) > snow_sim_water(t-1);     %If the refreezing for day t is larger than the water in the snowpack the day before, then the refreezing is limited
                  refreez(t)= snow_sim_water(t-1);      %Can't freez more water than is accumulated in the snowpack
              end
              snow_sim(t)=P(t)*Scf+snow_sim(t-1)+refreez(t);     %The total simulated snowpack for any given day is the precipitation that day together with snow pack from day before and refreeze of that day.
              snow_sim_water(t)=snow_sim_water(t-1)-refreez(t);        %The total simulated amount of water in the snowpack is the water in the snowpack the day before minus the water refrozen the same day
          else %T(t) > TT                   %temperature above threshold temperature, snowmelt will occur
              Melt(t)=as(t)*(T(t)-TT);           %Equations for melting rate of existing snowpack
              if Melt(t) > snow_sim(t-1);    %If the melting rate for day t is larger than the snowpack the day before, then the melting is limited
                  Melt(t)= snow_sim(t-1);     %Because it can't melt more snow than is available
              end
              snow_sim(t)=snow_sim(t-1)-Melt(t);                  %Total simulated snow is the simulated snowpack for the day before minus the melted snow
              snow_sim_water(t)=snow_sim_water(t-1)+P(t)+Melt(t);       %Total water amount in snow is the water amount in snow for the day before plus the precipitation and the melted snow
              if Cwh*snow_sim(t) < snow_sim_water(t);                 %The snowpack can retain as much as 10% of its water equivalent, but not more
                  runoff(t)=snow_sim_water(t)-0.1*snow_sim(t);        %if there is more liquid water, this goes to runoff (note:if there is no snowpack all water will go to runoff
                  snow_sim_water(t)=0.1*snow_sim(t);
              end
          end
      end
      snow_sim_total=snow_sim+snow_sim_water;                   %The total simulated snowpack is the water in snow and the simulated snowpack
      daynr=1:length(P);