X values in the Muskingum parameter ranges between (0 to 0.5) and it represents wedge storage. K is the time of travel between the inflow and outflow. Is there any possibilities to estimate K without flow data and with the support of other data.
Just a quick reminder about trade-off between accuracy and simplicity of a flood routing methods:
Muskingum type methods (hydrologic routing) is only solving mass balance, whereas "Dynamic Wave", "Diffusive Wave" and "Kinematic Wave" are solving mass and momentum balance (in full or with simplifications), those methods are called "hydraulic routing". Hydrologic routing is simple and inaccurate, only good for rough estimation, even if you have gauge data for calibration it has its limits. In lack of gauge data you can run "hydraulic routing" methods and then calibrate your Muskingum, however, if you do the effort and building a hydraulic routing method, then why you use Muskingum?
Just a quick reminder about trade-off between accuracy and simplicity of a flood routing methods:
Muskingum type methods (hydrologic routing) is only solving mass balance, whereas "Dynamic Wave", "Diffusive Wave" and "Kinematic Wave" are solving mass and momentum balance (in full or with simplifications), those methods are called "hydraulic routing". Hydrologic routing is simple and inaccurate, only good for rough estimation, even if you have gauge data for calibration it has its limits. In lack of gauge data you can run "hydraulic routing" methods and then calibrate your Muskingum, however, if you do the effort and building a hydraulic routing method, then why you use Muskingum?
I would simply use Manning's equation based on the expected mean flow, slope, and type and geometry of the channel to compute the mean flow velocity. With this computed velocity and the length of the channel reach, you can obtain the travel time. You can partition this calculation into various sub-reaches for varying topography. If there is no flow estimation from hydrologic calculations upstream, assuming a reasonable flow depth given the channel's geometry should provide a good-enough approximation.
Muskingum routing need rigorous calibration and validation for identification of parameters( K and X),where as you can use X=0.5(1-(qo/(so c delx)), where, qo=specific discharge, so=bed slope, c=kinematic wave celerity and del x= characteristic reach length, which leads to Muskingum Cunge Routing method..
In the absence of flow measurements, Muskingam parameters, K and X, can be estimated from channel characteristics.
K = L/Vw Where L is channel Length and Vw is flood wave velocity
Vw = I / B (dQ/dy), where B is top width of the water surface and dQ/dy is the slope of the discharge rating curve at a representative channel cross section. As an alternative, flood wave velocity can be taken as 1.33 – 1.67 times the average velocity, which may be estimated with Manning’s equation and representative cross section geometric information.
Estimate X as
X=1/2(1-Qo /(B So c ∆X))
Where Qo is average value of hydrograph (mid way between Qmax and Qmin), B is top width of flow area, So is friction slope or bed slope, c is flood wave speed, and ∆x is the length of reach.
For further details you may refer into ‘Technical Reference manual (Chapter 8, page 82 and 83) of HEC-HMS’.